Search for blocks/addresses/...

Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι → ι be given.
Let x3 of type ι → ι → ι be given.
Let x4 of type ι → ι → ι be given.
Let x5 of type ι → ι → ι be given.
Let x6 of type ι → ο be given.
Let x7 of type ι → ο be given.
Assume H0: 8f64a.. x0 x2 x4 x6 = 8f64a.. x1 x3 x5 x7.
Claim L1: x1 = f482f.. (8f64a.. x0 x2 x4 x6) 4a7ef..
Apply unknownprop_ff6492fe89763cba333f1d5dfd2add9c5dcebce46fae5cf3351072b0d2b148aa with 8f64a.. x0 x2 x4 x6, x1, x3, x5, x7.
The subproof is completed by applying H0.
Claim L2: x0 = x1
Apply L1 with λ x8 x9 . x0 = x9.
The subproof is completed by applying unknownprop_36c42de3fa64ba0d931d2bce5c95c24271e7ca12e15351b214ce939787147f70 with x0, x2, x4, x6.
Apply and4I with x0 = x1, ∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x2 x8 x9 = x3 x8 x9, ∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x4 x8 x9 = x5 x8 x9, ∀ x8 . prim1 x8 x0 ⟶ x6 x8 = x7 x8 leaving 4 subgoals.
The subproof is completed by applying L2.
Let x8 of type ι be given.
Assume H3: prim1 x8 x0.
Let x9 of type ι be given.
Assume H4: prim1 x9 x0.
Apply unknownprop_4e842e2c30ccf0c3564e02682ecde09675764a8b5663da987f76b91e34225304 with x0, x2, x4, x6, x8, x9, λ x10 x11 . x11 = x3 x8 x9 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Claim L5: prim1 x8 x1
Apply L2 with λ x10 x11 . prim1 x8 x10.
The subproof is completed by applying H3.
Claim L6: prim1 x9 x1
Apply L2 with λ x10 x11 . prim1 x9 x10.
The subproof is completed by applying H4.
Apply H0 with λ x10 x11 . e3162.. (f482f.. x11 (4ae4a.. 4a7ef..)) x8 x9 = x3 x8 x9.
Let x10 of type ι → ι → ο be given.
Apply unknownprop_4e842e2c30ccf0c3564e02682ecde09675764a8b5663da987f76b91e34225304 with x1, x3, x5, x7, x8, x9, λ x11 x12 . x10 x12 x11 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L6.
Let x8 of type ι be given.
Assume H3: prim1 x8 x0.
Let x9 of type ι be given.
Assume H4: prim1 x9 x0.
Apply unknownprop_521087284df84a924fcf4bcd5859c5772f0f0c1ecfc3853224d5653fe7e0ef2c with x0, x2, x4, x6, x8, x9, λ x10 x11 . x11 = x5 x8 x9 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Claim L5: prim1 x8 x1
Apply L2 with λ x10 x11 . prim1 x8 x10.
The subproof is completed by applying H3.
Claim L6: prim1 x9 x1
Apply L2 with λ x10 x11 . prim1 x9 x10.
The subproof is completed by applying H4.
Apply H0 with λ x10 x11 . e3162.. (f482f.. x11 (4ae4a.. (4ae4a.. 4a7ef..))) x8 x9 = x5 x8 x9.
Let x10 of type ι → ι → ο be given.
Apply unknownprop_521087284df84a924fcf4bcd5859c5772f0f0c1ecfc3853224d5653fe7e0ef2c with x1, x3, x5, x7, x8, x9, λ x11 x12 . x10 x12 x11 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L6.
Let x8 of type ι be given.
Assume H3: prim1 x8 x0.
Apply unknownprop_cd131d10c369b276d5ab02bbaa6503cd63c1cdda813ea32dfc1d611915267593 with x0, x2, x4, x6, x8, λ x9 x10 : ο . x10 = x7 x8 leaving 2 subgoals.
The subproof is completed by applying H3.
Claim L4: prim1 x8 x1
Apply L2 with λ x9 x10 . prim1 x8 x9.
The subproof is completed by applying H3.
Apply H0 with λ x9 x10 . decode_p (f482f.. x10 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x8 = x7 x8.
Let x9 of type ο → ο → ο be given.
Apply unknownprop_cd131d10c369b276d5ab02bbaa6503cd63c1cdda813ea32dfc1d611915267593 with x1, x3, x5, x7, x8, λ x10 x11 : ο . x9 x11 x10.
The subproof is completed by applying L4.
■