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.
Assume H0: bij x0 x1 x2.
Apply H0 with bij x1 x0 (inv x0 x2).
Assume H1: and (∀ x3 . x3x0x2 x3x1) (∀ x3 . x3x0∀ x4 . x4x0x2 x3 = x2 x4x3 = x4).
Apply H1 with (∀ x3 . x3x1∃ x4 . and (x4x0) (x2 x4 = x3))bij x1 x0 (inv x0 x2).
Assume H2: ∀ x3 . x3x0x2 x3x1.
Assume H3: ∀ x3 . x3x0∀ x4 . x4x0x2 x3 = x2 x4x3 = x4.
Assume H4: ∀ x3 . x3x1∃ x4 . and (x4x0) (x2 x4 = x3).
Claim L5: ...
...
Apply and3I with ∀ x3 . x3x1(λ x4 . prim0 (λ x5 . and (x5x0) (x2 x5 = x4))) x3x0, ∀ x3 . x3x1∀ x4 . x4x1(λ x5 . prim0 (λ x6 . and (x6x0) (x2 x6 = x5))) x3 = (λ x5 . prim0 (λ x6 . and (x6x0) (x2 x6 = x5))) x4x3 = x4, ∀ x3 . x3x0∃ x4 . and (x4x1) ((λ x5 . prim0 (λ x6 . and (x6x0) (x2 x6 = x5))) x4 = x3) leaving 3 subgoals.
Let x3 of type ι be given.
Assume H6: x3x1.
Apply L5 with x3, (λ x4 . prim0 (λ x5 . and (x5x0) (x2 x5 = x4))) x3x0 leaving 2 subgoals.
The subproof is completed by applying H6.
Assume H7: prim0 (λ x4 . and (x4x0) (x2 x4 = x3))x0.
Assume H8: x2 (prim0 (λ x4 . and (x4x0) (x2 x4 = x3))) = x3.
The subproof is completed by applying H7.
Let x3 of type ι be given.
Assume H6: x3x1.
Let x4 of type ι be given.
Assume H7: x4x1.
Assume H8: (λ x5 . prim0 (λ x6 . and (x6x0) (x2 x6 = x5))) x3 = (λ x5 . prim0 (λ x6 . and (x6x0) (x2 x6 = x5))) x4.
Apply L5 with x3, x3 = x4 leaving 2 subgoals.
The subproof is completed by applying H6.
Assume H9: (λ x5 . prim0 (λ x6 . and (x6x0) (x2 x6 = x5))) x3x0.
Assume H10: x2 ((λ x5 . prim0 (λ x6 . and (x6x0) ...)) ...) = ....
...
...