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Proofgold Proposition

∀ 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 . x7x0∀ x8 . x8x0∀ x9 . x9x0∀ x10 . x10x0x6 x7 x8 = x6 x9 x10and (x7 = x9) (x8 = x10))∀ x7 : ο . ((∀ x8 . x8x0∀ x9 . x9x0x6 x8 x9ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6)(∀ x8 . x8x0∀ x9 . x9x0prim0 (λ x11 . ∀ x12 : ο . (x11x0(∀ x13 : ο . (∀ x14 . and (x14x0) (x6 x8 x9 = x6 x11 x14)x13)x13)x12)x12) = x8)(∀ x8 . x8x0∀ x9 . x9x0prim0 (λ x11 . ∀ x12 : ο . (x11x0x6 x8 x9 = x6 (prim0 (λ x14 . ∀ x15 : ο . (x14x0(∀ x16 : ο . (∀ x17 . and (x17x0) (x6 x8 x9 = x6 x14 x17)x16)x16)x15)x15)) x11x12)x12) = x9)(∀ x8 . x8ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6prim0 (λ x9 . ∀ x10 : ο . (x9x0(∀ x11 : ο . (∀ x12 . and (x12x0) (x8 = x6 x9 x12)x11)x11)x10)x10)x0)(∀ x8 . x8ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6prim0 (λ x9 . ∀ x10 : ο . (x9x0x8 = x6 (prim0 (λ x12 . ∀ x13 : ο . (x12x0(∀ x14 : ο . (∀ x15 . and (x15x0) (x8 = x6 x12 x15)x14)x14)x13)x13)) x9x10)x10)x0)(∀ x8 . x8ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6∀ x9 . x9ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6prim0 (λ x11 . ∀ x12 : ο . (x11x0(∀ x13 : ο . (∀ x14 . and (x14x0) (x8 = x6 x11 x14)x13)x13)x12)x12) = prim0 (λ x11 . ∀ x12 : ο . (x11x0(∀ x13 : ο . (∀ x14 . and (x14x0) (x9 = x6 x11 x14)x13)x13)x12)x12)prim0 (λ x11 . ∀ x12 : ο . (x11x0x8 = x6 (prim0 (λ x14 . ∀ x15 : ο . (x14x0(∀ x16 : ο . (∀ x17 . and (x17x0) (x8 = x6 x14 x17)x16)x16)x15)x15)) x11x12)x12) = prim0 (λ x11 . ∀ x12 : ο . (x11x0x9 = x6 (prim0 (λ x14 . ∀ x15 : ο . (x14x0(∀ x16 : ο . (∀ x17 . and (x17x0) (x9 = x6 x14 x17)x16)x16)x15)x15)) x11x12)x12)x8 = x9)x6 x1 x1ReplSep2 x0 (λ x8 . x0) (λ x8 x9 . True) x6x6 x2 x1ReplSep2 x0 (λ x8 . x0) (λ x8 x9 . True) x6(∀ x8 . x8ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6∀ x9 . x9ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6x6 (x3 (prim0 (λ x10 . ∀ x11 : ο . (x10x0(∀ x12 : ο . (∀ x13 . and (x13x0) (x8 = x6 x10 x13)x12)x12)x11)x11)) (prim0 (λ x10 . ∀ x11 : ο . (x10x0(∀ x12 : ο . (∀ x13 . and (x13x0) (x9 = x6 x10 x13)x12)x12)x11)x11))) (x3 (prim0 (λ x10 . ∀ x11 : ο . (x10x0x8 = x6 (prim0 (λ x13 . ∀ x14 : ο . (x13x0(∀ x15 : ο . (∀ x16 . and (x16x0) (x8 = x6 x13 x16)x15)x15)x14)x14)) x10x11)x11)) (prim0 (λ x10 . ∀ x11 : ο . (x10x0x9 = x6 (prim0 (λ x13 . ∀ x14 : ο . (x13x0(∀ x15 : ο . (∀ x16 . and (x16x0) (x9 = x6 x13 x16)x15)x15)x14)x14)) x10x11)x11)))ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6)(∀ x8 . x8ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6∀ x9 . x9ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6prim0 (λ x11 . ∀ x12 : ο . (x11x0(∀ x13 : ο . (∀ x14 . and (x14x0) (x6 (x3 (prim0 (λ x16 . ∀ x17 : ο . (x16x0(∀ x18 : ο . (∀ x19 . and (x19x0) (x8 = x6 x16 x19)x18)x18)x17)x17)) (prim0 (λ x16 . ∀ x17 : ο . (x16x0(∀ x18 : ο . (∀ x19 . and (x19x0) (x9 = x6 x16 x19)x18)x18)x17)x17))) (x3 (prim0 (λ x16 . ∀ x17 : ο . (x16x0x8 = x6 (prim0 (λ x19 . ∀ x20 : ο . (x19x0(∀ x21 : ο . (∀ x22 . and (x22x0) (x8 = x6 x19 x22)x21)x21)x20)x20)) x16x17)x17)) (prim0 (λ x16 . ∀ x17 : ο . (x16x0x9 = x6 (prim0 (λ x19 . ∀ x20 : ο . (x19x0(∀ x21 : ο . (∀ x22 . and (x22x0) (x9 = x6 x19 x22)x21)x21)x20)x20)) x16x17)x17))) = x6 x11 x14)x13)x13)x12)x12) = x3 (prim0 (λ x11 . ∀ x12 : ο . (x11x0(∀ x13 : ο . (∀ x14 . and (x14x0) (x8 = x6 x11 x14)x13)x13)x12)x12)) (prim0 (λ x11 . ∀ x12 : ο . (x11x0(∀ x13 : ο . (∀ x14 . and (x14x0) (x9 = x6 x11 x14)x13)x13)x12)x12)))(∀ x8 . x8ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6∀ x9 . x9ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6prim0 (λ x11 . ∀ x12 : ο . (x11x0x6 (x3 (prim0 (λ x14 . ∀ x15 : ο . (x14x0(∀ x16 : ο . (∀ x17 . and (x17x0) (x8 = x6 x14 x17)x16)x16)x15)x15)) (prim0 (λ x14 . ∀ x15 : ο . (x14x0(∀ x16 : ο . (∀ x17 . and (x17x0) (x9 = x6 x14 x17)x16)x16)x15)x15))) (x3 (prim0 (λ x14 . ∀ x15 : ο . (x14x0x8 = x6 (prim0 (λ x17 . ∀ x18 : ο . (x17x0(∀ x19 : ο . (∀ x20 . and (x20x0) (x8 = x6 x17 x20)x19)x19)x18)x18)) x14x15)x15)) (prim0 (λ x14 . ∀ x15 : ο . (x14x0x9 = x6 (prim0 (λ x17 . ∀ x18 : ο . (x17x0(∀ x19 : ο . (∀ x20 . and (x20x0) (x9 = x6 x17 x20)x19)x19)x18)x18)) x14x15)x15))) = x6 (prim0 (λ x14 . ∀ x15 : ο . (x14x0(∀ x16 : ο . (∀ x17 . and (x17x0) (x6 (x3 (prim0 (λ x19 . ∀ x20 : ο . (x19x0(∀ x21 : ο . (∀ x22 . and (x22x0) (x8 = x6 x19 x22)x21)x21)x20)x20)) (prim0 (λ x19 . ∀ x20 : ο . (x19x0(∀ x21 : ο . (∀ x22 . and (x22x0) (x9 = x6 x19 x22)x21)x21)x20)x20))) (x3 (prim0 (λ x19 . ∀ x20 : ο . (x19x0x8 = x6 (prim0 (λ x22 . ∀ x23 : ο . (x22x0(∀ x24 : ο . (∀ x25 . and (x25x0) (x8 = x6 x22 x25)x24)x24)x23)x23)) x19x20)x20)) (prim0 (λ x19 . ∀ x20 : ο . (x19x0x9 = x6 (prim0 (λ x22 . ∀ x23 : ο . (x22x0(∀ x24 : ο . (∀ x25 . and (x25x0) (x9 = x6 x22 x25)x24)x24)x23)x23)) x19x20)x20))) = x6 x14 x17)x16)x16)x15)x15)) x11x12)x12) = x3 (prim0 (λ x11 . ∀ x12 : ο . (x11x0x8 = x6 (prim0 (λ x14 . ∀ x15 : ο . (x14x0(∀ x16 : ο . (∀ x17 . and (x17x0) (x8 = x6 x14 x17)x16)x16)x15)x15)) x11x12)x12)) (prim0 (λ x11 . ∀ x12 : ο . (x11x0x9 = x6 (prim0 (λ x14 . ∀ x15 : ο . (x14x0(∀ x16 : ο . (∀ x17 . and (x17x0) (x9 = x6 x14 x17)x16)x16)x15)x15)) x11x12)x12)))(∀ x8 . x8ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6∀ x9 . x9ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6x6 (x3 (x4 (prim0 (λ x10 . ∀ x11 : ο . (x10x0(∀ x12 : ο . (∀ x13 . and (x13x0) (x8 = x6 x10 x13)x12)x12)x11)x11)) (prim0 (λ x10 . ∀ x11 : ο . (x10x0(∀ x12 : ο . (∀ x13 . and (x13x0) (x9 = x6 x10 x13)x12)x12)x11)x11))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x10 . ∀ x11 : ο . (x10x0x8 = x6 (prim0 (λ x13 . ∀ x14 : ο . (x13x0(∀ x15 : ο . (∀ x16 . and (x16x0) (x8 = x6 x13 x16)x15)x15)x14)x14)) x10x11)x11)) (prim0 (λ x10 . ∀ x11 : ο . (x10x0x9 = x6 (prim0 (λ x13 . ∀ x14 : ο . (x13x0(∀ x15 : ο . (∀ x16 . and (x16x0) (x9 = x6 x13 x16)x15)x15)x14)x14)) x10x11)x11))))) (x3 (x4 (prim0 (λ x10 . ∀ x11 : ο . (x10x0(∀ x12 : ο . (∀ x13 . and (x13x0) (x8 = x6 x10 x13)x12)x12)x11)x11)) (prim0 (λ x10 . ∀ x11 : ο . (x10x0x9 = x6 (prim0 (λ x13 . ∀ x14 : ο . (x13x0(∀ x15 : ο . (∀ x16 . and (x16x0) (x9 = x6 x13 x16)x15)x15)x14)x14)) x10x11)x11))) (x4 (prim0 (λ x10 . ∀ x11 : ο . (x10x0x8 = x6 (prim0 (λ x13 . ∀ x14 : ο . (x13x0(∀ x15 : ο . (∀ x16 . and (x16x0) (x8 = x6 x13 x16)x15)x15)x14)x14)) x10x11)x11)) (prim0 (λ x10 . ∀ x11 : ο . (x10x0(∀ x12 : ο . (∀ x13 . and (x13x0) (x9 = x6 x10 x13)x12)x12)x11)x11))))ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6)(∀ x8 . x8ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6∀ x9 . x9ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6prim0 (λ x11 . ∀ x12 : ο . (x11x0(∀ x13 : ο . (∀ x14 . and (x14x0) (x6 (x3 (x4 (prim0 (λ x16 . ∀ x17 : ο . (x16x0(∀ x18 : ο . (∀ x19 . and (x19x0) (x8 = x6 x16 x19)x18)x18)x17)x17)) (prim0 (λ x16 . ∀ x17 : ο . (x16x0(∀ x18 : ο . (∀ x19 . and (x19x0) (x9 = x6 x16 x19)x18)x18)x17)x17))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x16 . ∀ x17 : ο . (x16x0x8 = x6 (prim0 (λ x19 . ∀ x20 : ο . (x19x0(∀ x21 : ο . (∀ x22 . and (x22x0) (x8 = x6 x19 x22)x21)x21)x20)x20)) x16x17)x17)) (prim0 (λ x16 . ∀ x17 : ο . (x16x0x9 = x6 (prim0 (λ x19 . ∀ x20 : ο . (x19x0(∀ x21 : ο . (∀ x22 . and (x22x0) (x9 = x6 x19 x22)x21)x21)x20)x20)) x16x17)x17))))) (x3 (x4 (prim0 (λ x16 . ∀ x17 : ο . (x16x0(∀ x18 : ο . (∀ x19 . and (x19x0) (x8 = x6 x16 x19)x18)x18)x17)x17)) (prim0 (λ x16 . ∀ x17 : ο . (x16x0x9 = x6 (prim0 (λ x19 . ∀ x20 : ο . (x19x0(∀ x21 : ο . (∀ x22 . and (x22x0) (x9 = x6 x19 x22)x21)x21)x20)x20)) x16x17)x17))) (x4 (prim0 (λ x16 . ∀ x17 : ο . (x16x0x8 = x6 (prim0 (λ x19 . ∀ x20 : ο . (x19x0(∀ x21 : ο . (∀ x22 . and (x22x0) (x8 = x6 x19 x22)x21)x21)x20)x20)) x16x17)x17)) (prim0 (λ x16 . ∀ x17 : ο . (x16x0(∀ x18 : ο . (∀ x19 . and (x19x0) (x9 = x6 x16 x19)x18)x18)x17)x17)))) = x6 x11 x14)x13)x13)x12)x12) = x3 (x4 (prim0 (λ x11 . ∀ x12 : ο . (x11x0(∀ x13 : ο . (∀ x14 . and (x14x0) (x8 = x6 x11 x14)x13)x13)x12)x12)) (prim0 (λ x11 . ∀ x12 : ο . (x11x0(∀ x13 : ο . (∀ x14 . and (x14x0) (x9 = x6 x11 x14)x13)x13)x12)x12))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x11 . ∀ x12 : ο . (x11x0x8 = x6 (prim0 (λ x14 . ∀ x15 : ο . (x14x0(∀ x16 : ο . (∀ x17 . and (x17x0) (x8 = x6 x14 x17)x16)x16)x15)x15)) x11x12)x12)) (prim0 (λ x11 . ∀ x12 : ο . (x11x0x9 = x6 (prim0 (λ x14 . ∀ x15 : ο . (x14x0(∀ x16 : ο . (∀ x17 . and (x17x0) (x9 = x6 x14 x17)x16)x16)x15)x15)) x11x12)x12)))))(∀ x8 . x8ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6∀ x9 . x9ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6prim0 (λ x11 . ∀ x12 : ο . (x11x0x6 (x3 (x4 (prim0 (λ x14 . ∀ x15 : ο . (x14x0(∀ x16 : ο . (∀ x17 . and (x17x0) (x8 = x6 x14 x17)x16)x16)x15)x15)) (prim0 (λ x14 . ∀ x15 : ο . (x14x0(∀ x16 : ο . (∀ x17 . and (x17x0) (x9 = x6 x14 x17)x16)x16)x15)x15))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x14 . ∀ x15 : ο . (x14x0x8 = x6 (prim0 (λ x17 . ∀ x18 : ο . (x17x0(∀ x19 : ο . (∀ x20 . and (x20x0) (x8 = x6 x17 x20)x19)x19)x18)x18)) x14x15)x15)) (prim0 (λ x14 . ∀ x15 : ο . (x14x0x9 = x6 (prim0 (λ x17 . ∀ x18 : ο . (x17x0(∀ x19 : ο . (∀ x20 . and (x20x0) (x9 = x6 x17 x20)x19)x19)x18)x18)) x14x15)x15))))) (x3 (x4 (prim0 (λ x14 . ∀ x15 : ο . (x14x0(∀ x16 : ο . (∀ x17 . and (x17x0) (x8 = x6 x14 x17)x16)x16)x15)x15)) (prim0 (λ x14 . ∀ x15 : ο . (x14x0x9 = x6 (prim0 (λ x17 . ∀ x18 : ο . (x17x0(∀ x19 : ο . (∀ x20 . and (x20x0) (x9 = x6 x17 x20)x19)x19)x18)x18)) x14x15)x15))) (x4 (prim0 (λ x14 . ∀ x15 : ο . (x14x0x8 = x6 (prim0 (λ x17 . ∀ x18 : ο . (x17x0(∀ x19 : ο . (∀ x20 . and (x20x0) (x8 = x6 x17 x20)x19)x19)x18)x18)) x14x15)x15)) (prim0 (λ x14 . ∀ x15 : ο . (x14x0(∀ x16 : ο . (∀ x17 . and (x17x0) (x9 = x6 x14 x17)x16)x16)x15)x15)))) = x6 (prim0 (λ x14 . ∀ x15 : ο . (x14x0(∀ x16 : ο . (∀ x17 . and (x17x0) (x6 (x3 (x4 (prim0 (λ x19 . ∀ x20 : ο . (x19x0(∀ x21 : ο . (∀ x22 . and (x22x0) (x8 = x6 x19 x22)x21)x21)x20)x20)) (prim0 (λ x19 . ∀ x20 : ο . (x19x0(∀ x21 : ο . (∀ x22 . and (x22x0) (x9 = x6 x19 x22)x21)x21)x20)x20))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x19 . ∀ x20 : ο . (x19x0x8 = x6 (prim0 (λ x22 . ∀ x23 : ο . (x22x0(∀ x24 : ο . (∀ x25 . and (x25x0) (x8 = x6 x22 x25)x24)x24)x23)x23)) x19x20)x20)) (prim0 (λ x19 . ∀ x20 : ο . (x19x0x9 = x6 (prim0 (λ x22 . ∀ x23 : ο . (x22x0(∀ x24 : ο . (∀ x25 . and (x25x0) (x9 = x6 x22 x25)x24)x24)x23)x23)) x19x20)x20))))) (x3 (x4 (prim0 (λ x19 . ∀ x20 : ο . (x19x0(∀ x21 : ο . (∀ x22 . and (x22x0) (x8 = x6 x19 x22)x21)x21)x20)x20)) (prim0 (λ x19 . ∀ x20 : ο . (x19x0x9 = x6 (prim0 (λ x22 . ∀ x23 : ο . (x22x0(∀ x24 : ο . (∀ x25 . and (x25x0) (x9 = x6 x22 x25)x24)x24)x23)x23)) x19x20)x20))) (x4 (prim0 (λ x19 . ∀ x20 : ο . (x19x0x8 = x6 (prim0 (λ x22 . ∀ x23 : ο . (x22x0(∀ x24 : ο . (∀ x25 . and (x25x0) (x8 = x6 x22 x25)x24)x24)x23)x23)) x19x20)x20)) (prim0 (λ x19 . ∀ x20 : ο . (x19x0(∀ x21 : ο . (∀ x22 . and (x22x0) (x9 = x6 x19 x22)x21)x21)x20)x20)))) = x6 x14 x17)x16)x16)x15)x15)) x11x12)x12) = x3 (x4 (prim0 (λ x11 . ∀ x12 : ο . (x11x0(∀ x13 : ο . (∀ x14 . and (x14x0) (x8 = x6 x11 x14)x13)x13)x12)x12)) (prim0 (λ x11 . ∀ x12 : ο . (x11x0x9 = x6 (prim0 (λ x14 . ∀ x15 : ο . (x14x0(∀ x16 : ο . (∀ x17 . and (x17x0) (x9 = x6 x14 x17)x16)x16)x15)x15)) x11x12)x12))) (x4 (prim0 (λ x11 . ∀ x12 : ο . (x11x0x8 = x6 (prim0 (λ x14 . ∀ x15 : ο . (x14x0(∀ x16 : ο . (∀ x17 . and (x17x0) (x8 = x6 x14 x17)x16)x16)x15)x15)) x11x12)x12)) (prim0 (λ x11 . ∀ x12 : ο . (x11x0(∀ x13 : ο . (∀ x14 . and (x14x0) (x9 = x6 x11 x14)x13)x13)x12)x12))))x7)x7
type
prop
theory
HotG
name
-
proof
PUJkc..
Megalodon
-
proofgold address
TMYzs..
creator
4969 Pr6Pc../7e419..
owner
4969 Pr6Pc../7e419..
term root
11029..