Search for blocks/addresses/...

Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: 80242.. x0.
Assume H1: 80242.. x1.
Assume H2: Subq (e4431.. x0) (e4431.. x1).
Assume H3: ∀ x2 . prim1 x2 (e4431.. x0) ⟶ iff (prim1 x2 x0) (prim1 x2 x1).
Apply unknownprop_90012ae02c7e97888ea4d0a930b01b500b9d0d1d1a0841df69b82a77726b906b with x0, Subq x0 x1 leaving 2 subgoals.
The subproof is completed by applying H0.
Assume H4: Subq x0 (472ec.. (e4431.. x0)).
Assume H5: ∀ x2 . prim1 x2 (e4431.. x0) ⟶ exactly1of2 (prim1 ((λ x3 . 15418.. x3 (91630.. (4ae4a.. 4a7ef..))) x2) x0) (prim1 x2 x0).
Apply unknownprop_90012ae02c7e97888ea4d0a930b01b500b9d0d1d1a0841df69b82a77726b906b with x1, Subq x0 x1 leaving 2 subgoals.
The subproof is completed by applying H1.
Assume H6: Subq x1 (472ec.. (e4431.. x1)).
Assume H7: ∀ x2 . prim1 x2 (e4431.. x1) ⟶ exactly1of2 (prim1 ((λ x3 . 15418.. x3 (91630.. (4ae4a.. 4a7ef..))) x2) x1) (prim1 x2 x1).
Let x2 of type ι be given.
Assume H8: prim1 x2 x0.
Claim L9: ...
...
Apply unknownprop_b46721c187c37140cbae22d356b00ba89f4126d81d8665e4be15b5a58c78d06f with e4431.. x0, 94f9e.. (e4431.. x0) (λ x3 . (λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3), x2, prim1 x2 x1 leaving 3 subgoals.
The subproof is completed by applying L9.
Assume H10: prim1 x2 (e4431.. x0).
Apply H3 with x2, prim1 x2 x1 leaving 2 subgoals.
The subproof is completed by applying H10.
Assume H11: prim1 x2 x0 ⟶ prim1 x2 x1.
Assume H12: prim1 x2 x1 ⟶ prim1 x2 x0.
Apply H11.
The subproof is completed by applying H8.
Assume H10: prim1 x2 (94f9e.. (e4431.. x0) (λ x3 . (λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3)).
Apply unknownprop_d908b89102f7b662c739e5a844f67efc8ae1cd05a2e9ce1e3546fa3885f40100 with e4431.. x0, λ x3 . (λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3, x2, prim1 x2 x1 leaving 2 subgoals.
The subproof is completed by applying H10.
Let x3 of type ι be given.
Assume H11: prim1 x3 (e4431.. x0).
Assume H12: x2 = (λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3.
Claim L13: ...
...
Apply exactly1of2_E with prim1 ((λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3) x1, prim1 x3 x1, prim1 x2 x1 leaving 3 subgoals.
Apply H7 with x3.
The subproof is completed by applying L13.
Assume H14: prim1 ((λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3) x1.
Assume H15: nIn x3 x1.
Apply H12 with λ x4 x5 . prim1 x5 x1.
The subproof is completed by applying H14.
Assume H14: nIn ((λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3) x1.
Assume H15: prim1 x3 x1.
Apply FalseE with prim1 x2 x1.
Apply exactly1of2_E with prim1 ((λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3) x0, prim1 x3 x0, False leaving 3 subgoals.
Apply H5 with x3.
The subproof is completed by applying H11.
Assume H16: prim1 ((λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3) x0.
Assume H17: nIn x3 x0.
Apply H17.
Apply H3 with x3, prim1 x3 x0 leaving 2 subgoals.
The subproof is completed by applying H11.
Assume H18: prim1 ... ... ⟶ prim1 x3 x1.
...
...
■