Search for blocks/addresses/...

Proofgold Proof

pf
Let x0 of type ι be given.
Apply and3I with ∀ x1 . prim1 x1 x0prim1 x1 x0, ∀ x1 . prim1 x1 x0∀ x2 . prim1 x2 x0x1 = x2x1 = x2, ∀ x1 . prim1 x1 x0∃ x2 . and (prim1 x2 x0) (x2 = x1) leaving 3 subgoals.
Let x1 of type ι be given.
Assume H0: prim1 x1 x0.
The subproof is completed by applying H0.
Let x1 of type ι be given.
Assume H0: prim1 x1 x0.
Let x2 of type ι be given.
Assume H1: prim1 x2 x0.
Assume H2: x1 = x2.
The subproof is completed by applying H2.
Let x1 of type ι be given.
Assume H0: prim1 x1 x0.
Let x2 of type ο be given.
Assume H1: ∀ x3 . and (prim1 x3 x0) (x3 = x1)x2.
Apply H1 with x1.
Apply andI with prim1 x1 x0, x1 = x1 leaving 2 subgoals.
The subproof is completed by applying H0.
Let x3 of type ιιο be given.
Assume H2: x3 x1 x1.
The subproof is completed by applying H2.