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Proofgold Signed Transaction

vin
PrJAV../57527..
PUWYu../97a90..
vout
PrJAV../123fe.. 6.48 bars
TMFn1../bf5c1.. ownership of 6b23b.. as prop with payaddr Pr6Pc.. rights free controlledby Pr6Pc.. upto 0
TMJrc../bf78d.. ownership of e6660.. as prop with payaddr Pr6Pc.. rights free controlledby Pr6Pc.. upto 0
TMYzs../7e419.. ownership of 455b2.. as prop with payaddr Pr6Pc.. rights free controlledby Pr6Pc.. upto 0
TMUxU../ea8b9.. ownership of 11029.. as prop with payaddr Pr6Pc.. rights free controlledby Pr6Pc.. upto 0
PUJkc../5f2a5.. doc published by Pr6Pc..
Param explicit_Realsexplicit_Reals : ι → ι → ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ο) → ο
Definition andand := λ x0 x1 : ο . ∀ x2 : ο . (x0 ⟶ x1 ⟶ x2) ⟶ x2
Param ReplSep2ReplSep2 : ι → (ι → ι) → (ι → ι → ο) → CT2 ι
Param TrueTrue : ο
Param SepSep : ι → (ι → ο) → ι
Param explicit_Field_minusexplicit_Field_minus : ι → ι → ι → (ι → ι → ι) → (ι → ι → ι) → ι → ι
Known 89287.. : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . ∀ x5 : ι → ι → ο . ∀ x6 : ι → ι → ι . explicit_Reals x0 x1 x2 x3 x4 x5 ⟶ (∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ x6 x7 x8 = x6 x9 x10 ⟶ and (x7 = x9) (x8 = x10)) ⟶ ∀ x7 : ο . ((∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ x6 x8 x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ ∀ x9 : ι → ο . (∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ x8 = x6 x10 x11 ⟶ x9 (x6 x10 x11)) ⟶ x9 x8) ⟶ (∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x6 x8 x9 = x6 x11 x13) ⟶ x12) ⟶ x12)) = x8) ⟶ (∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ prim0 (λ x11 . and (x11 ∈ x0) (x6 x8 x9 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x6 x8 x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)) = x9) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x8 = x6 x9 x11) ⟶ x10) ⟶ x10)) ∈ x0) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ prim0 (λ x9 . and (x9 ∈ x0) (x8 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9)) ∈ x0) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ x8 = x6 (prim0 (λ x10 . and (x10 ∈ x0) (∀ x11 : ο . (∀ x12 . and (x12 ∈ x0) (x8 = x6 x10 x12) ⟶ x11) ⟶ x11))) (prim0 (λ x10 . and (x10 ∈ x0) (x8 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x8 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10)))) ⟶ (∀ x8 . x8 ∈ x0 ⟶ x6 x8 x1 ∈ {x9 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6|x6 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x9 = x6 x11 x13) ⟶ x12) ⟶ x12))) x1 = x9}) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ ∀ x9 . x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6 ⟶ prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12)) = prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x9 = x6 x11 x13) ⟶ x12) ⟶ x12)) ⟶ prim0 (λ x11 . and (x11 ∈ x0) (x8 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)) = prim0 (λ x11 . and (x11 ∈ x0) (x9 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)) ⟶ x8 = x9) ⟶ x6 x1 x1 ∈ ReplSep2 x0 (λ x8 . x0) (λ x8 x9 . True) x6 ⟶ x6 x2 x1 ∈ ReplSep2 x0 (λ x8 . x0) (λ x8 x9 . True) x6 ⟶ (∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ x6 (x3 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x6 x8 x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x6 x10 x11 = x6 x13 x15) ⟶ x14) ⟶ x14)))) (x3 (prim0 (λ x13 . and (x13 ∈ x0) (x6 x8 x9 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x6 x8 x9 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13))) (prim0 (λ x13 . and (x13 ∈ x0) (x6 x10 x11 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x6 x10 x11 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13)))) = x6 (x3 x8 x10) (x3 x9 x11)) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ ∀ x9 . x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6 ⟶ x6 (x3 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x9 = x6 x11 x13) ⟶ x12) ⟶ x12)))) (x3 (prim0 (λ x11 . and (x11 ∈ x0) (x8 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11))) (prim0 (λ x11 . and (x11 ∈ x0) (x9 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)))) = x6 (x3 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x9 = x6 x11 x13) ⟶ x12) ⟶ x12)))) (x3 (prim0 (λ x11 . and (x11 ∈ x0) (x8 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11))) (prim0 (λ x11 . and (x11 ∈ x0) (x9 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11))))) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ ∀ x9 . x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6 ⟶ x6 (x3 (prim0 (λ x10 . and (x10 ∈ x0) (∀ x11 : ο . (∀ x12 . and (x12 ∈ x0) (x8 = x6 x10 x12) ⟶ x11) ⟶ x11))) (prim0 (λ x10 . and (x10 ∈ x0) (∀ x11 : ο . (∀ x12 . and (x12 ∈ x0) (x9 = x6 x10 x12) ⟶ x11) ⟶ x11)))) (x3 (prim0 (λ x10 . and (x10 ∈ x0) (x8 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x8 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10))) (prim0 (λ x10 . and (x10 ∈ x0) (x9 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x9 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10)))) ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ ∀ x9 . x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6 ⟶ prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x6 (x3 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x8 = x6 x15 x17) ⟶ x16) ⟶ x16))) (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x9 = x6 x15 x17) ⟶ x16) ⟶ x16)))) (x3 (prim0 (λ x15 . and (x15 ∈ x0) (x8 = x6 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x8 = x6 x17 x19) ⟶ x18) ⟶ x18))) x15))) (prim0 (λ x15 . and (x15 ∈ x0) (x9 = x6 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x9 = x6 x17 x19) ⟶ x18) ⟶ x18))) x15)))) = x6 x11 x13) ⟶ x12) ⟶ x12)) = x3 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x9 = x6 x11 x13) ⟶ x12) ⟶ x12)))) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ ∀ x9 . x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6 ⟶ prim0 (λ x11 . and (x11 ∈ x0) (x6 (x3 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14)))) (x3 (prim0 (λ x13 . and (x13 ∈ x0) (x8 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x8 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13))) (prim0 (λ x13 . and (x13 ∈ x0) (x9 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x9 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13)))) = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x6 (x3 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x8 = x6 x17 x19) ⟶ x18) ⟶ x18))) (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x9 = x6 x17 x19) ⟶ x18) ⟶ x18)))) (x3 (prim0 (λ x17 . and (x17 ∈ x0) (x8 = x6 (prim0 (λ x19 . and (x19 ∈ x0) (∀ x20 : ο . (∀ x21 . and (x21 ∈ x0) (x8 = x6 x19 x21) ⟶ x20) ⟶ x20))) x17))) (prim0 (λ x17 . and (x17 ∈ x0) (x9 = x6 (prim0 (λ x19 . and (x19 ∈ x0) (∀ x20 : ο . (∀ x21 . and (x21 ∈ x0) (x9 = x6 x19 x21) ⟶ x20) ⟶ x20))) x17)))) = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)) = x3 (prim0 (λ x11 . and (x11 ∈ x0) (x8 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11))) (prim0 (λ x11 . and (x11 ∈ x0) (x9 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)))) ⟶ (∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ x6 (x3 (x4 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x6 x8 x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x6 x10 x11 = x6 x13 x15) ⟶ x14) ⟶ x14)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x13 . and (x13 ∈ x0) (x6 x8 x9 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x6 x8 x9 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13))) (prim0 (λ x13 . and (x13 ∈ x0) (x6 x10 x11 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x6 x10 x11 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13)))))) (x3 (x4 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x6 x8 x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) (prim0 (λ x13 . and (x13 ∈ x0) (x6 x10 x11 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x6 x10 x11 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13)))) (x4 (prim0 (λ x13 . and (x13 ∈ x0) (x6 x8 x9 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x6 x8 x9 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13))) (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x6 x10 x11 = x6 x13 x15) ⟶ x14) ⟶ x14))))) = x6 (x3 (x4 x8 x10) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 x9 x11))) (x3 (x4 x8 x11) (x4 x9 x10))) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ ∀ x9 . x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6 ⟶ x6 (x3 (x4 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x9 = x6 x11 x13) ⟶ x12) ⟶ x12)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x11 . and (x11 ∈ x0) (x8 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11))) (prim0 (λ x11 . and (x11 ∈ x0) (x9 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)))))) (x3 (x4 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) (prim0 (λ x11 . and (x11 ∈ x0) (x9 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)))) (x4 (prim0 (λ x11 . and (x11 ∈ x0) (x8 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11))) (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x9 = x6 x11 x13) ⟶ x12) ⟶ x12))))) = x6 (x3 (x4 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x9 = x6 x11 x13) ⟶ x12) ⟶ x12)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x11 . and (x11 ∈ x0) (x8 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11))) (prim0 (λ x11 . and (x11 ∈ x0) (x9 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)))))) (x3 (x4 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) (prim0 (λ x11 . and (x11 ∈ x0) (x9 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)))) (x4 (prim0 (λ x11 . and (x11 ∈ x0) (x8 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11))) (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x9 = x6 x11 x13) ⟶ x12) ⟶ x12)))))) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ ∀ x9 . x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6 ⟶ x3 (x4 (prim0 (λ x10 . and (x10 ∈ x0) (∀ x11 : ο . (∀ x12 . and (x12 ∈ x0) (x8 = x6 x10 x12) ⟶ x11) ⟶ x11))) (prim0 (λ x10 . and (x10 ∈ x0) (∀ x11 : ο . (∀ x12 . and (x12 ∈ x0) (x9 = x6 x10 x12) ⟶ x11) ⟶ x11)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x10 . and (x10 ∈ x0) (x8 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x8 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10))) (prim0 (λ x10 . and (x10 ∈ x0) (x9 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x9 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10))))) ∈ x0) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ ∀ x9 . x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6 ⟶ x3 (x4 (prim0 (λ x10 . and (x10 ∈ x0) (∀ x11 : ο . (∀ x12 . and (x12 ∈ x0) (x8 = x6 x10 x12) ⟶ x11) ⟶ x11))) (prim0 (λ x10 . and (x10 ∈ x0) (x9 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x9 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10)))) (x4 (prim0 (λ x10 . and (x10 ∈ x0) (x8 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x8 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10))) (prim0 (λ x10 . and (x10 ∈ x0) (∀ x11 : ο . (∀ x12 . and (x12 ∈ x0) (x9 = x6 x10 x12) ⟶ x11) ⟶ x11)))) ∈ x0) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ ∀ x9 . x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6 ⟶ x6 (x3 (x4 (prim0 (λ x10 . and (x10 ∈ x0) (∀ x11 : ο . (∀ x12 . and (x12 ∈ x0) (x8 = x6 x10 x12) ⟶ x11) ⟶ x11))) (prim0 (λ x10 . and (x10 ∈ x0) (∀ x11 : ο . (∀ x12 . and (x12 ∈ x0) (x9 = x6 x10 x12) ⟶ x11) ⟶ x11)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x10 . and (x10 ∈ x0) (x8 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x8 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10))) (prim0 (λ x10 . and (x10 ∈ x0) (x9 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x9 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10)))))) (x3 (x4 (prim0 (λ x10 . and (x10 ∈ x0) (∀ x11 : ο . (∀ x12 . and (x12 ∈ x0) (x8 = x6 x10 x12) ⟶ x11) ⟶ x11))) (prim0 (λ x10 . and (x10 ∈ x0) (x9 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x9 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10)))) (x4 (prim0 (λ x10 . and (x10 ∈ x0) (x8 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x8 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10))) (prim0 (λ x10 . and (x10 ∈ x0) (∀ x11 : ο . (∀ x12 . and (x12 ∈ x0) (x9 = x6 x10 x12) ⟶ x11) ⟶ x11))))) ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ ∀ x9 . x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6 ⟶ prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x6 (x3 (x4 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x8 = x6 x15 x17) ⟶ x16) ⟶ x16))) (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x9 = x6 x15 x17) ⟶ x16) ⟶ x16)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x15 . and (x15 ∈ x0) (x8 = x6 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x8 = x6 x17 x19) ⟶ x18) ⟶ x18))) x15))) (prim0 (λ x15 . and (x15 ∈ x0) (x9 = x6 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x9 = x6 x17 x19) ⟶ x18) ⟶ x18))) x15)))))) (x3 (x4 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x8 = x6 x15 x17) ⟶ x16) ⟶ x16))) (prim0 (λ x15 . and (x15 ∈ x0) (x9 = x6 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x9 = x6 x17 x19) ⟶ x18) ⟶ x18))) x15)))) (x4 (prim0 (λ x15 . and (x15 ∈ x0) (x8 = x6 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x8 = x6 x17 x19) ⟶ x18) ⟶ x18))) x15))) (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x9 = x6 x15 x17) ⟶ x16) ⟶ x16))))) = x6 x11 x13) ⟶ x12) ⟶ x12)) = x3 (x4 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x9 = x6 x11 x13) ⟶ x12) ⟶ x12)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x11 . and (x11 ∈ x0) (x8 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11))) (prim0 (λ x11 . and (x11 ∈ x0) (x9 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)))))) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ ∀ x9 . x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6 ⟶ prim0 (λ x11 . and (x11 ∈ x0) (x6 (x3 (x4 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x13 . and (x13 ∈ x0) (x8 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x8 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13))) (prim0 (λ x13 . and (x13 ∈ x0) (x9 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x9 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13)))))) (x3 (x4 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) (prim0 (λ x13 . and (x13 ∈ x0) (x9 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x9 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13)))) (x4 (prim0 (λ x13 . and (x13 ∈ x0) (x8 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x8 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13))) (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14))))) = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x6 (x3 (x4 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x8 = x6 x17 x19) ⟶ x18) ⟶ x18))) (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x9 = x6 x17 x19) ⟶ x18) ⟶ x18)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x17 . and (x17 ∈ x0) (x8 = x6 (prim0 (λ x19 . and (x19 ∈ x0) (∀ x20 : ο . (∀ x21 . and (x21 ∈ x0) (x8 = x6 x19 x21) ⟶ x20) ⟶ x20))) x17))) (prim0 (λ x17 . and (x17 ∈ x0) (x9 = x6 (prim0 (λ x19 . and (x19 ∈ x0) (∀ x20 : ο . (∀ x21 . and (x21 ∈ x0) (x9 = x6 x19 x21) ⟶ x20) ⟶ x20))) x17)))))) (x3 (x4 (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x8 = x6 x17 x19) ⟶ x18) ⟶ x18))) (prim0 (λ x17 . and (x17 ∈ x0) (x9 = x6 (prim0 (λ x19 . and (x19 ∈ x0) (∀ x20 : ο . (∀ x21 . and (x21 ∈ x0) (x9 = x6 x19 x21) ⟶ x20) ⟶ x20))) x17)))) (x4 (prim0 (λ x17 . and (x17 ∈ x0) (x8 = x6 (prim0 (λ x19 . and (x19 ∈ x0) (∀ x20 : ο . (∀ x21 . and (x21 ∈ x0) (x8 = x6 x19 x21) ⟶ x20) ⟶ x20))) x17))) (prim0 (λ x17 . and (x17 ∈ x0) (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x9 = x6 x17 x19) ⟶ x18) ⟶ x18))))) = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)) = x3 (x4 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) (prim0 (λ x11 . and (x11 ∈ x0) (x9 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x9 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11)))) (x4 (prim0 (λ x11 . and (x11 ∈ x0) (x8 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x8 = x6 x13 x15) ⟶ x14) ⟶ x14))) x11))) (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x9 = x6 x11 x13) ⟶ x12) ⟶ x12))))) ⟶ x7) ⟶ x7
Theorem 455b2.. : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . ∀ x5 : ι → ι → ο . ∀ x6 : ι → ι → ι . explicit_Reals x0 x1 x2 x3 x4 x5 ⟶ (∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ x6 x7 x8 = x6 x9 x10 ⟶ and (x7 = x9) (x8 = x10)) ⟶ ∀ x7 : ο . ((∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ x6 x8 x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6) ⟶ (∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ prim0 (λ x11 . ∀ x12 : ο . (x11 ∈ x0 ⟶ (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x6 x8 x9 = x6 x11 x14) ⟶ x13) ⟶ x13) ⟶ x12) ⟶ x12) = x8) ⟶ (∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ prim0 (λ x11 . ∀ x12 : ο . (x11 ∈ x0 ⟶ x6 x8 x9 = x6 (prim0 (λ x14 . ∀ x15 : ο . (x14 ∈ x0 ⟶ (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x6 x8 x9 = x6 x14 x17) ⟶ x16) ⟶ x16) ⟶ x15) ⟶ x15)) x11 ⟶ x12) ⟶ x12) = x9) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ prim0 (λ x9 . ∀ x10 : ο . (x9 ∈ x0 ⟶ (∀ x11 : ο . (∀ x12 . and (x12 ∈ x0) (x8 = x6 x9 x12) ⟶ x11) ⟶ x11) ⟶ x10) ⟶ x10) ∈ x0) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ prim0 (λ x9 . ∀ x10 : ο . (x9 ∈ x0 ⟶ x8 = x6 (prim0 (λ x12 . ∀ x13 : ο . (x12 ∈ x0 ⟶ (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x8 = x6 x12 x15) ⟶ x14) ⟶ x14) ⟶ x13) ⟶ x13)) x9 ⟶ x10) ⟶ x10) ∈ x0) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ ∀ x9 . x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6 ⟶ prim0 (λ x11 . ∀ x12 : ο . (x11 ∈ x0 ⟶ (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x8 = x6 x11 x14) ⟶ x13) ⟶ x13) ⟶ x12) ⟶ x12) = prim0 (λ x11 . ∀ x12 : ο . (x11 ∈ x0 ⟶ (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x9 = x6 x11 x14) ⟶ x13) ⟶ x13) ⟶ x12) ⟶ x12) ⟶ prim0 (λ x11 . ∀ x12 : ο . (x11 ∈ x0 ⟶ x8 = x6 (prim0 (λ x14 . ∀ x15 : ο . (x14 ∈ x0 ⟶ (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x8 = x6 x14 x17) ⟶ x16) ⟶ x16) ⟶ x15) ⟶ x15)) x11 ⟶ x12) ⟶ x12) = prim0 (λ x11 . ∀ x12 : ο . (x11 ∈ x0 ⟶ x9 = x6 (prim0 (λ x14 . ∀ x15 : ο . (x14 ∈ x0 ⟶ (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x9 = x6 x14 x17) ⟶ x16) ⟶ x16) ⟶ x15) ⟶ x15)) x11 ⟶ x12) ⟶ x12) ⟶ x8 = x9) ⟶ x6 x1 x1 ∈ ReplSep2 x0 (λ x8 . x0) (λ x8 x9 . True) x6 ⟶ x6 x2 x1 ∈ ReplSep2 x0 (λ x8 . x0) (λ x8 x9 . True) x6 ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ ∀ x9 . x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6 ⟶ x6 (x3 (prim0 (λ x10 . ∀ x11 : ο . (x10 ∈ x0 ⟶ (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x10 x13) ⟶ x12) ⟶ x12) ⟶ x11) ⟶ x11)) (prim0 (λ x10 . ∀ x11 : ο . (x10 ∈ x0 ⟶ (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x9 = x6 x10 x13) ⟶ x12) ⟶ x12) ⟶ x11) ⟶ x11))) (x3 (prim0 (λ x10 . ∀ x11 : ο . (x10 ∈ x0 ⟶ x8 = x6 (prim0 (λ x13 . ∀ x14 : ο . (x13 ∈ x0 ⟶ (∀ x15 : ο . (∀ x16 . and (x16 ∈ x0) (x8 = x6 x13 x16) ⟶ x15) ⟶ x15) ⟶ x14) ⟶ x14)) x10 ⟶ x11) ⟶ x11)) (prim0 (λ x10 . ∀ x11 : ο . (x10 ∈ x0 ⟶ x9 = x6 (prim0 (λ x13 . ∀ x14 : ο . (x13 ∈ x0 ⟶ (∀ x15 : ο . (∀ x16 . and (x16 ∈ x0) (x9 = x6 x13 x16) ⟶ x15) ⟶ x15) ⟶ x14) ⟶ x14)) x10 ⟶ x11) ⟶ x11))) ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ ∀ x9 . x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6 ⟶ prim0 (λ x11 . ∀ x12 : ο . (x11 ∈ x0 ⟶ (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x6 (x3 (prim0 (λ x16 . ∀ x17 : ο . (x16 ∈ x0 ⟶ (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x8 = x6 x16 x19) ⟶ x18) ⟶ x18) ⟶ x17) ⟶ x17)) (prim0 (λ x16 . ∀ x17 : ο . (x16 ∈ x0 ⟶ (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x9 = x6 x16 x19) ⟶ x18) ⟶ x18) ⟶ x17) ⟶ x17))) (x3 (prim0 (λ x16 . ∀ x17 : ο . (x16 ∈ x0 ⟶ x8 = x6 (prim0 (λ x19 . ∀ x20 : ο . (x19 ∈ x0 ⟶ (∀ x21 : ο . (∀ x22 . and (x22 ∈ x0) (x8 = x6 x19 x22) ⟶ x21) ⟶ x21) ⟶ x20) ⟶ x20)) x16 ⟶ x17) ⟶ x17)) (prim0 (λ x16 . ∀ x17 : ο . (x16 ∈ x0 ⟶ x9 = x6 (prim0 (λ x19 . ∀ x20 : ο . (x19 ∈ x0 ⟶ (∀ x21 : ο . (∀ x22 . and (x22 ∈ x0) (x9 = x6 x19 x22) ⟶ x21) ⟶ x21) ⟶ x20) ⟶ x20)) x16 ⟶ x17) ⟶ x17))) = x6 x11 x14) ⟶ x13) ⟶ x13) ⟶ x12) ⟶ x12) = x3 (prim0 (λ x11 . ∀ x12 : ο . (x11 ∈ x0 ⟶ (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x8 = x6 x11 x14) ⟶ x13) ⟶ x13) ⟶ x12) ⟶ x12)) (prim0 (λ x11 . ∀ x12 : ο . (x11 ∈ x0 ⟶ (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x9 = x6 x11 x14) ⟶ x13) ⟶ x13) ⟶ x12) ⟶ x12))) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ ∀ x9 . x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6 ⟶ prim0 (λ x11 . ∀ x12 : ο . (x11 ∈ x0 ⟶ x6 (x3 (prim0 (λ x14 . ∀ x15 : ο . (x14 ∈ x0 ⟶ (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x8 = x6 x14 x17) ⟶ x16) ⟶ x16) ⟶ x15) ⟶ x15)) (prim0 (λ x14 . ∀ x15 : ο . (x14 ∈ x0 ⟶ (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x9 = x6 x14 x17) ⟶ x16) ⟶ x16) ⟶ x15) ⟶ x15))) (x3 (prim0 (λ x14 . ∀ x15 : ο . (x14 ∈ x0 ⟶ x8 = x6 (prim0 (λ x17 . ∀ x18 : ο . (x17 ∈ x0 ⟶ (∀ x19 : ο . (∀ x20 . and (x20 ∈ x0) (x8 = x6 x17 x20) ⟶ x19) ⟶ x19) ⟶ x18) ⟶ x18)) x14 ⟶ x15) ⟶ x15)) (prim0 (λ x14 . ∀ x15 : ο . (x14 ∈ x0 ⟶ x9 = x6 (prim0 (λ x17 . ∀ x18 : ο . (x17 ∈ x0 ⟶ (∀ x19 : ο . (∀ x20 . and (x20 ∈ x0) (x9 = x6 x17 x20) ⟶ x19) ⟶ x19) ⟶ x18) ⟶ x18)) x14 ⟶ x15) ⟶ x15))) = x6 (prim0 (λ x14 . ∀ x15 : ο . (x14 ∈ x0 ⟶ (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x6 (x3 (prim0 (λ x19 . ∀ x20 : ο . (x19 ∈ x0 ⟶ (∀ x21 : ο . (∀ x22 . and (x22 ∈ x0) (x8 = x6 x19 x22) ⟶ x21) ⟶ x21) ⟶ x20) ⟶ x20)) (prim0 (λ x19 . ∀ x20 : ο . (x19 ∈ x0 ⟶ (∀ x21 : ο . (∀ x22 . and (x22 ∈ x0) (x9 = x6 x19 x22) ⟶ x21) ⟶ x21) ⟶ x20) ⟶ x20))) (x3 (prim0 (λ x19 . ∀ x20 : ο . (x19 ∈ x0 ⟶ x8 = x6 (prim0 (λ x22 . ∀ x23 : ο . (x22 ∈ x0 ⟶ (∀ x24 : ο . (∀ x25 . and (x25 ∈ x0) (x8 = x6 x22 x25) ⟶ x24) ⟶ x24) ⟶ x23) ⟶ x23)) x19 ⟶ x20) ⟶ x20)) (prim0 (λ x19 . ∀ x20 : ο . (x19 ∈ x0 ⟶ x9 = x6 (prim0 (λ x22 . ∀ x23 : ο . (x22 ∈ x0 ⟶ (∀ x24 : ο . (∀ x25 . and (x25 ∈ x0) (x9 = x6 x22 x25) ⟶ x24) ⟶ x24) ⟶ x23) ⟶ x23)) x19 ⟶ x20) ⟶ x20))) = x6 x14 x17) ⟶ x16) ⟶ x16) ⟶ x15) ⟶ x15)) x11 ⟶ x12) ⟶ x12) = x3 (prim0 (λ x11 . ∀ x12 : ο . (x11 ∈ x0 ⟶ x8 = x6 (prim0 (λ x14 . ∀ x15 : ο . (x14 ∈ x0 ⟶ (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x8 = x6 x14 x17) ⟶ x16) ⟶ x16) ⟶ x15) ⟶ x15)) x11 ⟶ x12) ⟶ x12)) (prim0 (λ x11 . ∀ x12 : ο . (x11 ∈ x0 ⟶ x9 = x6 (prim0 (λ x14 . ∀ x15 : ο . (x14 ∈ x0 ⟶ (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x9 = x6 x14 x17) ⟶ x16) ⟶ x16) ⟶ x15) ⟶ x15)) x11 ⟶ x12) ⟶ x12))) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ ∀ x9 . x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6 ⟶ x6 (x3 (x4 (prim0 (λ x10 . ∀ x11 : ο . (x10 ∈ x0 ⟶ (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x10 x13) ⟶ x12) ⟶ x12) ⟶ x11) ⟶ x11)) (prim0 (λ x10 . ∀ x11 : ο . (x10 ∈ x0 ⟶ (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x9 = x6 x10 x13) ⟶ x12) ⟶ x12) ⟶ x11) ⟶ x11))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x10 . ∀ x11 : ο . (x10 ∈ x0 ⟶ x8 = x6 (prim0 (λ x13 . ∀ x14 : ο . (x13 ∈ x0 ⟶ (∀ x15 : ο . (∀ x16 . and (x16 ∈ x0) (x8 = x6 x13 x16) ⟶ x15) ⟶ x15) ⟶ x14) ⟶ x14)) x10 ⟶ x11) ⟶ x11)) (prim0 (λ x10 . ∀ x11 : ο . (x10 ∈ x0 ⟶ x9 = x6 (prim0 (λ x13 . ∀ x14 : ο . (x13 ∈ x0 ⟶ (∀ x15 : ο . (∀ x16 . and (x16 ∈ x0) (x9 = x6 x13 x16) ⟶ x15) ⟶ x15) ⟶ x14) ⟶ x14)) x10 ⟶ x11) ⟶ x11))))) (x3 (x4 (prim0 (λ x10 . ∀ x11 : ο . (x10 ∈ x0 ⟶ (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x10 x13) ⟶ x12) ⟶ x12) ⟶ x11) ⟶ x11)) (prim0 (λ x10 . ∀ x11 : ο . (x10 ∈ x0 ⟶ x9 = x6 (prim0 (λ x13 . ∀ x14 : ο . (x13 ∈ x0 ⟶ (∀ x15 : ο . (∀ x16 . and (x16 ∈ x0) (x9 = x6 x13 x16) ⟶ x15) ⟶ x15) ⟶ x14) ⟶ x14)) x10 ⟶ x11) ⟶ x11))) (x4 (prim0 (λ x10 . ∀ x11 : ο . (x10 ∈ x0 ⟶ x8 = x6 (prim0 (λ x13 . ∀ x14 : ο . (x13 ∈ x0 ⟶ (∀ x15 : ο . (∀ x16 . and (x16 ∈ x0) (x8 = x6 x13 x16) ⟶ x15) ⟶ x15) ⟶ x14) ⟶ x14)) x10 ⟶ x11) ⟶ x11)) (prim0 (λ x10 . ∀ x11 : ο . (x10 ∈ x0 ⟶ (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x9 = x6 x10 x13) ⟶ x12) ⟶ x12) ⟶ x11) ⟶ x11)))) ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ ∀ x9 . x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6 ⟶ prim0 (λ x11 . ∀ x12 : ο . (x11 ∈ x0 ⟶ (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x6 (x3 (x4 (prim0 (λ x16 . ∀ x17 : ο . (x16 ∈ x0 ⟶ (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x8 = x6 x16 x19) ⟶ x18) ⟶ x18) ⟶ x17) ⟶ x17)) (prim0 (λ x16 . ∀ x17 : ο . (x16 ∈ x0 ⟶ (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x9 = x6 x16 x19) ⟶ x18) ⟶ x18) ⟶ x17) ⟶ x17))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x16 . ∀ x17 : ο . (x16 ∈ x0 ⟶ x8 = x6 (prim0 (λ x19 . ∀ x20 : ο . (x19 ∈ x0 ⟶ (∀ x21 : ο . (∀ x22 . and (x22 ∈ x0) (x8 = x6 x19 x22) ⟶ x21) ⟶ x21) ⟶ x20) ⟶ x20)) x16 ⟶ x17) ⟶ x17)) (prim0 (λ x16 . ∀ x17 : ο . (x16 ∈ x0 ⟶ x9 = x6 (prim0 (λ x19 . ∀ x20 : ο . (x19 ∈ x0 ⟶ (∀ x21 : ο . (∀ x22 . and (x22 ∈ x0) (x9 = x6 x19 x22) ⟶ x21) ⟶ x21) ⟶ x20) ⟶ x20)) x16 ⟶ x17) ⟶ x17))))) (x3 (x4 (prim0 (λ x16 . ∀ x17 : ο . (x16 ∈ x0 ⟶ (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x8 = x6 x16 x19) ⟶ x18) ⟶ x18) ⟶ x17) ⟶ x17)) (prim0 (λ x16 . ∀ x17 : ο . (x16 ∈ x0 ⟶ x9 = x6 (prim0 (λ x19 . ∀ x20 : ο . (x19 ∈ x0 ⟶ (∀ x21 : ο . (∀ x22 . and (x22 ∈ x0) (x9 = x6 x19 x22) ⟶ x21) ⟶ x21) ⟶ x20) ⟶ x20)) x16 ⟶ x17) ⟶ x17))) (x4 (prim0 (λ x16 . ∀ x17 : ο . (x16 ∈ x0 ⟶ x8 = x6 (prim0 (λ x19 . ∀ x20 : ο . (x19 ∈ x0 ⟶ (∀ x21 : ο . (∀ x22 . and (x22 ∈ x0) (x8 = x6 x19 x22) ⟶ x21) ⟶ x21) ⟶ x20) ⟶ x20)) x16 ⟶ x17) ⟶ x17)) (prim0 (λ x16 . ∀ x17 : ο . (x16 ∈ x0 ⟶ (∀ x18 : ο . (∀ x19 . and (x19 ∈ x0) (x9 = x6 x16 x19) ⟶ x18) ⟶ x18) ⟶ x17) ⟶ x17)))) = x6 x11 x14) ⟶ x13) ⟶ x13) ⟶ x12) ⟶ x12) = x3 (x4 (prim0 (λ x11 . ∀ x12 : ο . (x11 ∈ x0 ⟶ (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x8 = x6 x11 x14) ⟶ x13) ⟶ x13) ⟶ x12) ⟶ x12)) (prim0 (λ x11 . ∀ x12 : ο . (x11 ∈ x0 ⟶ (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x9 = x6 x11 x14) ⟶ x13) ⟶ x13) ⟶ x12) ⟶ x12))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x11 . ∀ x12 : ο . (x11 ∈ x0 ⟶ x8 = x6 (prim0 (λ x14 . ∀ x15 : ο . (x14 ∈ x0 ⟶ (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x8 = x6 x14 x17) ⟶ x16) ⟶ x16) ⟶ x15) ⟶ x15)) x11 ⟶ x12) ⟶ x12)) (prim0 (λ x11 . ∀ x12 : ο . (x11 ∈ x0 ⟶ x9 = x6 (prim0 (λ x14 . ∀ x15 : ο . (x14 ∈ x0 ⟶ (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x9 = x6 x14 x17) ⟶ x16) ⟶ x16) ⟶ x15) ⟶ x15)) x11 ⟶ x12) ⟶ x12))))) ⟶ (∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ ∀ x9 . x9 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6 ⟶ prim0 (λ x11 . ∀ x12 : ο . (x11 ∈ x0 ⟶ x6 (x3 (x4 (prim0 (λ x14 . ∀ x15 : ο . (x14 ∈ x0 ⟶ (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x8 = x6 x14 x17) ⟶ x16) ⟶ x16) ⟶ x15) ⟶ x15)) (prim0 (λ x14 . ∀ x15 : ο . (x14 ∈ x0 ⟶ (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x9 = x6 x14 x17) ⟶ x16) ⟶ x16) ⟶ x15) ⟶ x15))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x14 . ∀ x15 : ο . (x14 ∈ x0 ⟶ x8 = x6 (prim0 (λ x17 . ∀ x18 : ο . (x17 ∈ x0 ⟶ (∀ x19 : ο . (∀ x20 . and (x20 ∈ x0) (x8 = x6 x17 x20) ⟶ x19) ⟶ x19) ⟶ x18) ⟶ x18)) x14 ⟶ x15) ⟶ x15)) (prim0 (λ x14 . ∀ x15 : ο . (x14 ∈ x0 ⟶ x9 = x6 (prim0 (λ x17 . ∀ x18 : ο . (x17 ∈ x0 ⟶ (∀ x19 : ο . (∀ x20 . and (x20 ∈ x0) (x9 = x6 x17 x20) ⟶ x19) ⟶ x19) ⟶ x18) ⟶ x18)) x14 ⟶ x15) ⟶ x15))))) (x3 (x4 (prim0 (λ x14 . ∀ x15 : ο . (x14 ∈ x0 ⟶ (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x8 = x6 x14 x17) ⟶ x16) ⟶ x16) ⟶ x15) ⟶ x15)) (prim0 (λ x14 . ∀ x15 : ο . (x14 ∈ x0 ⟶ x9 = x6 (prim0 (λ x17 . ∀ x18 : ο . (x17 ∈ x0 ⟶ (∀ x19 : ο . (∀ x20 . and (x20 ∈ x0) (x9 = x6 x17 x20) ⟶ x19) ⟶ x19) ⟶ x18) ⟶ x18)) x14 ⟶ x15) ⟶ x15))) (x4 (prim0 (λ x14 . ∀ x15 : ο . (x14 ∈ x0 ⟶ x8 = x6 (prim0 (λ x17 . ∀ x18 : ο . (x17 ∈ x0 ⟶ (∀ x19 : ο . (∀ x20 . and (x20 ∈ x0) (x8 = x6 x17 x20) ⟶ x19) ⟶ x19) ⟶ x18) ⟶ x18)) x14 ⟶ x15) ⟶ x15)) (prim0 (λ x14 . ∀ x15 : ο . (x14 ∈ x0 ⟶ (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x9 = x6 x14 x17) ⟶ x16) ⟶ x16) ⟶ x15) ⟶ x15)))) = x6 (prim0 (λ x14 . ∀ x15 : ο . (x14 ∈ x0 ⟶ (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x6 (x3 (x4 (prim0 (λ x19 . ∀ x20 : ο . (x19 ∈ x0 ⟶ (∀ x21 : ο . (∀ x22 . and (x22 ∈ x0) (x8 = x6 x19 x22) ⟶ x21) ⟶ x21) ⟶ x20) ⟶ x20)) (prim0 (λ x19 . ∀ x20 : ο . (x19 ∈ x0 ⟶ (∀ x21 : ο . (∀ x22 . and (x22 ∈ x0) (x9 = x6 x19 x22) ⟶ x21) ⟶ x21) ⟶ x20) ⟶ x20))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x19 . ∀ x20 : ο . (x19 ∈ x0 ⟶ x8 = x6 (prim0 (λ x22 . ∀ x23 : ο . (x22 ∈ x0 ⟶ (∀ x24 : ο . (∀ x25 . and (x25 ∈ x0) (x8 = x6 x22 x25) ⟶ x24) ⟶ x24) ⟶ x23) ⟶ x23)) x19 ⟶ x20) ⟶ x20)) (prim0 (λ x19 . ∀ x20 : ο . (x19 ∈ x0 ⟶ x9 = x6 (prim0 (λ x22 . ∀ x23 : ο . (x22 ∈ x0 ⟶ (∀ x24 : ο . (∀ x25 . and (x25 ∈ x0) (x9 = x6 x22 x25) ⟶ x24) ⟶ x24) ⟶ x23) ⟶ x23)) x19 ⟶ x20) ⟶ x20))))) (x3 (x4 (prim0 (λ x19 . ∀ x20 : ο . (x19 ∈ x0 ⟶ (∀ x21 : ο . (∀ x22 . and (x22 ∈ x0) (x8 = x6 x19 x22) ⟶ x21) ⟶ x21) ⟶ x20) ⟶ x20)) (prim0 (λ x19 . ∀ x20 : ο . (x19 ∈ x0 ⟶ x9 = x6 (prim0 (λ x22 . ∀ x23 : ο . (x22 ∈ x0 ⟶ (∀ x24 : ο . (∀ x25 . and (x25 ∈ x0) (x9 = x6 x22 x25) ⟶ x24) ⟶ x24) ⟶ x23) ⟶ x23)) x19 ⟶ x20) ⟶ x20))) (x4 (prim0 (λ x19 . ∀ x20 : ο . (x19 ∈ x0 ⟶ x8 = x6 (prim0 (λ x22 . ∀ x23 : ο . (x22 ∈ x0 ⟶ (∀ x24 : ο . (∀ x25 . and (x25 ∈ x0) (x8 = x6 x22 x25) ⟶ x24) ⟶ x24) ⟶ x23) ⟶ x23)) x19 ⟶ x20) ⟶ x20)) (prim0 (λ x19 . ∀ x20 : ο . (x19 ∈ x0 ⟶ (∀ x21 : ο . (∀ x22 . and (x22 ∈ x0) (x9 = x6 x19 x22) ⟶ x21) ⟶ x21) ⟶ x20) ⟶ x20)))) = x6 x14 x17) ⟶ x16) ⟶ x16) ⟶ x15) ⟶ x15)) x11 ⟶ x12) ⟶ x12) = x3 (x4 (prim0 (λ x11 . ∀ x12 : ο . (x11 ∈ x0 ⟶ (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x8 = x6 x11 x14) ⟶ x13) ⟶ x13) ⟶ x12) ⟶ x12)) (prim0 (λ x11 . ∀ x12 : ο . (x11 ∈ x0 ⟶ x9 = x6 (prim0 (λ x14 . ∀ x15 : ο . (x14 ∈ x0 ⟶ (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x9 = x6 x14 x17) ⟶ x16) ⟶ x16) ⟶ x15) ⟶ x15)) x11 ⟶ x12) ⟶ x12))) (x4 (prim0 (λ x11 . ∀ x12 : ο . (x11 ∈ x0 ⟶ x8 = x6 (prim0 (λ x14 . ∀ x15 : ο . (x14 ∈ x0 ⟶ (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x8 = x6 x14 x17) ⟶ x16) ⟶ x16) ⟶ x15) ⟶ x15)) x11 ⟶ x12) ⟶ x12)) (prim0 (λ x11 . ∀ x12 : ο . (x11 ∈ x0 ⟶ (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x9 = x6 x11 x14) ⟶ x13) ⟶ x13) ⟶ x12) ⟶ x12)))) ⟶ x7) ⟶ x7 (proof)
Param explicit_Fieldexplicit_Field : ι → ι → ι → (ι → ι → ι) → (ι → ι → ι) → ο
Param explicit_Complexexplicit_Complex : ι → (ι → ι) → (ι → ι) → ι → ι → ι → (ι → ι → ι) → (ι → ι → ι) → ο
Param SubqSubq : ι → ι → ο
Known 10d6b.. : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . ∀ x5 : ι → ι → ο . ∀ x6 : ι → ι → ι . explicit_Reals x0 x1 x2 x3 x4 x5 ⟶ (∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ x6 x7 x8 = x6 x9 x10 ⟶ and (x7 = x9) (x8 = x10)) ⟶ explicit_Field (ReplSep2 x0 (λ x7 . x0) (λ x7 x8 . True) x6) (x6 x1 x1) (x6 x2 x1) (λ x7 x8 . x6 (x3 (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x7 = x6 x9 x11) ⟶ x10) ⟶ x10))) (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x8 = x6 x9 x11) ⟶ x10) ⟶ x10)))) (x3 (prim0 (λ x9 . and (x9 ∈ x0) (x7 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x7 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9))) (prim0 (λ x9 . and (x9 ∈ x0) (x8 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9))))) (λ x7 x8 . x6 (x3 (x4 (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x7 = x6 x9 x11) ⟶ x10) ⟶ x10))) (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x8 = x6 x9 x11) ⟶ x10) ⟶ x10)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x9 . and (x9 ∈ x0) (x7 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x7 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9))) (prim0 (λ x9 . and (x9 ∈ x0) (x8 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9)))))) (x3 (x4 (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x7 = x6 x9 x11) ⟶ x10) ⟶ x10))) (prim0 (λ x9 . and (x9 ∈ x0) (x8 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9)))) (x4 (prim0 (λ x9 . and (x9 ∈ x0) (x7 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x7 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9))) (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x8 = x6 x9 x11) ⟶ x10) ⟶ x10)))))) ⟶ and (explicit_Complex (ReplSep2 x0 (λ x7 . x0) (λ x7 x8 . True) x6) (λ x7 . x6 (prim0 (λ x8 . and (x8 ∈ x0) (∀ x9 : ο . (∀ x10 . and (x10 ∈ x0) (x7 = x6 x8 x10) ⟶ x9) ⟶ x9))) x1) (λ x7 . x6 (prim0 (λ x8 . and (x8 ∈ x0) (x7 = x6 (prim0 (λ x10 . and (x10 ∈ x0) (∀ x11 : ο . (∀ x12 . and (x12 ∈ x0) (x7 = x6 x10 x12) ⟶ x11) ⟶ x11))) x8))) x1) (x6 x1 x1) (x6 x2 x1) (x6 x1 x2) (λ x7 x8 . x6 (x3 (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x7 = x6 x9 x11) ⟶ x10) ⟶ x10))) (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x8 = x6 x9 x11) ⟶ x10) ⟶ x10)))) (x3 (prim0 (λ x9 . and (x9 ∈ x0) (x7 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x7 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9))) (prim0 (λ x9 . and (x9 ∈ x0) (x8 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9))))) (λ x7 x8 . x6 (x3 (x4 (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x7 = x6 x9 x11) ⟶ x10) ⟶ x10))) (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x8 = x6 x9 x11) ⟶ x10) ⟶ x10)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x9 . and (x9 ∈ x0) (x7 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x7 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9))) (prim0 (λ x9 . and (x9 ∈ x0) (x8 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9)))))) (x3 (x4 (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x7 = x6 x9 x11) ⟶ x10) ⟶ x10))) (prim0 (λ x9 . and (x9 ∈ x0) (x8 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9)))) (x4 (prim0 (λ x9 . and (x9 ∈ x0) (x7 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x7 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9))) (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x8 = x6 x9 x11) ⟶ x10) ⟶ x10))))))) ((∀ x7 . x7 ∈ x0 ⟶ x6 x7 x1 = x7) ⟶ and (and (and (and (and (x0 ⊆ ReplSep2 x0 (λ x7 . x0) (λ x7 x8 . True) x6) (∀ x7 . x7 ∈ x0 ⟶ prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x7 = x6 x9 x11) ⟶ x10) ⟶ x10)) = x7)) (x6 x1 x1 = x1)) (x6 x2 x1 = x2)) (∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ x6 (x3 (prim0 (λ x10 . and (x10 ∈ x0) (∀ x11 : ο . (∀ x12 . and (x12 ∈ x0) (x7 = x6 x10 x12) ⟶ x11) ⟶ x11))) (prim0 (λ x10 . and (x10 ∈ x0) (∀ x11 : ο . (∀ x12 . and (x12 ∈ x0) (x8 = x6 x10 x12) ⟶ x11) ⟶ x11)))) (x3 (prim0 (λ x10 . and (x10 ∈ x0) (x7 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x7 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10))) (prim0 (λ x10 . and (x10 ∈ x0) (x8 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x8 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10)))) = x3 x7 x8)) (∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ x6 (x3 (x4 (prim0 (λ x10 . and (x10 ∈ x0) (∀ x11 : ο . (∀ x12 . and (x12 ∈ x0) (x7 = x6 x10 x12) ⟶ x11) ⟶ x11))) (prim0 (λ x10 . and (x10 ∈ x0) (∀ x11 : ο . (∀ x12 . and (x12 ∈ x0) (x8 = x6 x10 x12) ⟶ x11) ⟶ x11)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x10 . and (x10 ∈ x0) (x7 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x7 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10))) (prim0 (λ x10 . and (x10 ∈ x0) (x8 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x8 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10)))))) (x3 (x4 (prim0 (λ x10 . and (x10 ∈ x0) (∀ x11 : ο . (∀ x12 . and (x12 ∈ x0) (x7 = x6 x10 x12) ⟶ x11) ⟶ x11))) (prim0 (λ x10 . and (x10 ∈ x0) (x8 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x8 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10)))) (x4 (prim0 (λ x10 . and (x10 ∈ x0) (x7 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x7 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10))) (prim0 (λ x10 . and (x10 ∈ x0) (∀ x11 : ο . (∀ x12 . and (x12 ∈ x0) (x8 = x6 x10 x12) ⟶ x11) ⟶ x11))))) = x4 x7 x8))
Theorem 6b23b.. : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . ∀ x5 : ι → ι → ο . ∀ x6 : ι → ι → ι . explicit_Reals x0 x1 x2 x3 x4 x5 ⟶ (∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ x6 x7 x8 = x6 x9 x10 ⟶ and (x7 = x9) (x8 = x10)) ⟶ explicit_Field (ReplSep2 x0 (λ x7 . x0) (λ x7 x8 . True) x6) (x6 x1 x1) (x6 x2 x1) (λ x7 x8 . x6 (x3 (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x7 = x6 x9 x11) ⟶ x10) ⟶ x10))) (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x8 = x6 x9 x11) ⟶ x10) ⟶ x10)))) (x3 (prim0 (λ x9 . and (x9 ∈ x0) (x7 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x7 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9))) (prim0 (λ x9 . and (x9 ∈ x0) (x8 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9))))) (λ x7 x8 . x6 (x3 (x4 (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x7 = x6 x9 x11) ⟶ x10) ⟶ x10))) (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x8 = x6 x9 x11) ⟶ x10) ⟶ x10)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x9 . and (x9 ∈ x0) (x7 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x7 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9))) (prim0 (λ x9 . and (x9 ∈ x0) (x8 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9)))))) (x3 (x4 (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x7 = x6 x9 x11) ⟶ x10) ⟶ x10))) (prim0 (λ x9 . and (x9 ∈ x0) (x8 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9)))) (x4 (prim0 (λ x9 . and (x9 ∈ x0) (x7 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x7 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9))) (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x8 = x6 x9 x11) ⟶ x10) ⟶ x10)))))) ⟶ ∀ x7 : ο . (explicit_Complex (ReplSep2 x0 (λ x8 . x0) (λ x8 x9 . True) x6) (λ x8 . x6 (prim0 (λ x9 . and (x9 ∈ x0) (∀ x10 : ο . (∀ x11 . and (x11 ∈ x0) (x8 = x6 x9 x11) ⟶ x10) ⟶ x10))) x1) (λ x8 . x6 (prim0 (λ x9 . and (x9 ∈ x0) (x8 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∀ x12 : ο . (∀ x13 . and (x13 ∈ x0) (x8 = x6 x11 x13) ⟶ x12) ⟶ x12))) x9))) x1) (x6 x1 x1) (x6 x2 x1) (x6 x1 x2) (λ x8 x9 . x6 (x3 (prim0 (λ x10 . and (x10 ∈ x0) (∀ x11 : ο . (∀ x12 . and (x12 ∈ x0) (x8 = x6 x10 x12) ⟶ x11) ⟶ x11))) (prim0 (λ x10 . and (x10 ∈ x0) (∀ x11 : ο . (∀ x12 . and (x12 ∈ x0) (x9 = x6 x10 x12) ⟶ x11) ⟶ x11)))) (x3 (prim0 (λ x10 . and (x10 ∈ x0) (x8 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x8 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10))) (prim0 (λ x10 . and (x10 ∈ x0) (x9 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x9 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10))))) (λ x8 x9 . x6 (x3 (x4 (prim0 (λ x10 . and (x10 ∈ x0) (∀ x11 : ο . (∀ x12 . and (x12 ∈ x0) (x8 = x6 x10 x12) ⟶ x11) ⟶ x11))) (prim0 (λ x10 . and (x10 ∈ x0) (∀ x11 : ο . (∀ x12 . and (x12 ∈ x0) (x9 = x6 x10 x12) ⟶ x11) ⟶ x11)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x10 . and (x10 ∈ x0) (x8 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x8 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10))) (prim0 (λ x10 . and (x10 ∈ x0) (x9 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x9 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10)))))) (x3 (x4 (prim0 (λ x10 . and (x10 ∈ x0) (∀ x11 : ο . (∀ x12 . and (x12 ∈ x0) (x8 = x6 x10 x12) ⟶ x11) ⟶ x11))) (prim0 (λ x10 . and (x10 ∈ x0) (x9 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x9 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10)))) (x4 (prim0 (λ x10 . and (x10 ∈ x0) (x8 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x8 = x6 x12 x14) ⟶ x13) ⟶ x13))) x10))) (prim0 (λ x10 . and (x10 ∈ x0) (∀ x11 : ο . (∀ x12 . and (x12 ∈ x0) (x9 = x6 x10 x12) ⟶ x11) ⟶ x11)))))) ⟶ ((∀ x8 . x8 ∈ x0 ⟶ x6 x8 x1 = x8) ⟶ ∀ x8 : ο . ((∀ x9 : ο . ((∀ x10 : ο . ((∀ x11 : ο . ((∀ x12 : ο . (x0 ⊆ ReplSep2 x0 (λ x13 . x0) (λ x13 x14 . True) x6 ⟶ (∀ x13 . x13 ∈ x0 ⟶ prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x13 = x6 x15 x17) ⟶ x16) ⟶ x16)) = x13) ⟶ x12) ⟶ x12) ⟶ x6 x1 x1 = x1 ⟶ x11) ⟶ x11) ⟶ x6 x2 x1 = x2 ⟶ x10) ⟶ x10) ⟶ (∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ x6 (x3 (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x10 = x6 x13 x15) ⟶ x14) ⟶ x14))) (prim0 (λ x13 . and (x13 ∈ x0) (∀ x14 : ο . (∀ x15 . and (x15 ∈ x0) (x11 = x6 x13 x15) ⟶ x14) ⟶ x14)))) (x3 (prim0 (λ x13 . and (x13 ∈ x0) (x10 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x10 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13))) (prim0 (λ x13 . and (x13 ∈ x0) (x11 = x6 (prim0 (λ x15 . and (x15 ∈ x0) (∀ x16 : ο . (∀ x17 . and (x17 ∈ x0) (x11 = x6 x15 x17) ⟶ x16) ⟶ x16))) x13)))) = x3 x10 x11) ⟶ x9) ⟶ x9) ⟶ (∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ x6 (x3 (x4 (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x9 = x6 x12 x14) ⟶ x13) ⟶ x13))) (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x10 = x6 x12 x14) ⟶ x13) ⟶ x13)))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x12 . and (x12 ∈ x0) (x9 = x6 (prim0 (λ x14 . and (x14 ∈ x0) (∀ x15 : ο . (∀ x16 . and (x16 ∈ x0) (x9 = x6 x14 x16) ⟶ x15) ⟶ x15))) x12))) (prim0 (λ x12 . and (x12 ∈ x0) (x10 = x6 (prim0 (λ x14 . and (x14 ∈ x0) (∀ x15 : ο . (∀ x16 . and (x16 ∈ x0) (x10 = x6 x14 x16) ⟶ x15) ⟶ x15))) x12)))))) (x3 (x4 (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x9 = x6 x12 x14) ⟶ x13) ⟶ x13))) (prim0 (λ x12 . and (x12 ∈ x0) (x10 = x6 (prim0 (λ x14 . and (x14 ∈ x0) (∀ x15 : ο . (∀ x16 . and (x16 ∈ x0) (x10 = x6 x14 x16) ⟶ x15) ⟶ x15))) x12)))) (x4 (prim0 (λ x12 . and (x12 ∈ x0) (x9 = x6 (prim0 (λ x14 . and (x14 ∈ x0) (∀ x15 : ο . (∀ x16 . and (x16 ∈ x0) (x9 = x6 x14 x16) ⟶ x15) ⟶ x15))) x12))) (prim0 (λ x12 . and (x12 ∈ x0) (∀ x13 : ο . (∀ x14 . and (x14 ∈ x0) (x10 = x6 x12 x14) ⟶ x13) ⟶ x13))))) = x4 x9 x10) ⟶ x8) ⟶ x8) ⟶ x7) ⟶ x7 (proof)