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 ιι be given.
Let x3 of type ιι be given.
Assume H0: inj x0 x1 x2.
Assume H1: inj x1 x0 x3.
Apply H0 with c2e41.. x0 x1.
Assume H2: ∀ x4 . prim1 x4 x0prim1 (x2 x4) x1.
Assume H3: ∀ x4 . prim1 x4 x0∀ x5 . prim1 x5 x0x2 x4 = x2 x5x4 = x5.
Apply H1 with c2e41.. x0 x1.
Assume H4: ∀ x4 . prim1 x4 x1prim1 (x3 x4) x0.
Assume H5: ∀ x4 . prim1 x4 x1∀ x5 . prim1 x5 x1x3 x4 = x3 x5x4 = x5.
Claim L6: ...
...
Claim L7: ...
...
Apply unknownprop_1c03dbc8933f14179c6d1fab30498a3d9cfe087cf19262a1a909f1f505467ff7 with x0, λ x4 . 94f9e.. (1ad11.. x1 (94f9e.. (1ad11.. x0 x4) (λ x5 . x2 x5))) (λ x5 . x3 x5), c2e41.. x0 x1 leaving 3 subgoals.
The subproof is completed by applying L6.
The subproof is completed by applying L7.
Let x4 of type ι be given.
Assume H8: (λ x5 . and (prim1 x5 (e5b72.. x0)) (94f9e.. (1ad11.. x1 (94f9e.. (1ad11.. x0 x5) x2)) x3 = x5)) x4.
Apply H8 with c2e41.. x0 x1.
Assume H9: prim1 x4 (e5b72.. x0).
Assume H10: (λ x5 . 94f9e.. (1ad11.. x1 (94f9e.. (1ad11.. x0 x5) (λ x6 . x2 x6))) (λ x6 . x3 x6)) x4 = x4.
Apply unknownprop_4865425a7f56150b37062def658749568c73ac3811495e4e2624803c98cf736b with x0, x1, λ x5 . If_i (prim1 x5 x4) (inv x1 x3 x5) (x2 x5).
Apply and3I with ∀ x5 . prim1 x5 x0prim1 ((λ x6 . If_i (prim1 x6 x4) (inv x1 x3 x6) (x2 x6)) x5) x1, ∀ x5 . prim1 x5 x0∀ x6 . prim1 x6 x0(λ x7 . If_i (prim1 x7 x4) (inv x1 x3 x7) (x2 x7)) x5 = (λ x7 . If_i (prim1 x7 x4) (inv x1 x3 x7) (x2 x7)) x6x5 = x6, ∀ x5 . prim1 x5 x1∃ x6 . and (prim1 x6 x0) ((λ x7 . If_i (prim1 x7 x4) (inv x1 x3 x7) (x2 x7)) x6 = x5) leaving 3 subgoals.
Let x5 of type ι be given.
Assume H11: prim1 x5 x0.
Apply xm with prim1 x5 x4, prim1 (If_i (prim1 x5 x4) (inv x1 x3 x5) (x2 x5)) x1 leaving 2 subgoals.
Assume H12: prim1 x5 x4.
Apply If_i_1 with prim1 x5 x4, inv x1 x3 x5, x2 x5, λ x6 x7 . prim1 x7 x1 leaving 2 subgoals.
The subproof is completed by applying H12.
Claim L13: ...
...
Apply unknownprop_d908b89102f7b662c739e5a844f67efc8ae1cd05a2e9ce1e3546fa3885f40100 with 1ad11.. x1 (94f9e.. ... ...), ..., ..., ... leaving 2 subgoals.
...
...
...
...
...