Search for blocks/addresses/...

Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ιι be given.
Assume H0: ∀ x2 . x2x0∀ x3 . x3x0x1 x2 = x1 x3x2 = x3.
Let x2 of type ο be given.
Assume H1: ∀ x3 : ι → ι . bij x0 {x1 x4|x4 ∈ x0} x3x2.
Apply H1 with x1.
Apply bijI with x0, {x1 x3|x3 ∈ x0}, x1 leaving 3 subgoals.
The subproof is completed by applying ReplI with x0, x1.
The subproof is completed by applying H0.
Let x3 of type ι be given.
Assume H2: x3{x1 x4|x4 ∈ x0}.
Apply ReplE_impred with x0, x1, x3, ∃ x4 . and (x4x0) (x1 x4 = x3) leaving 2 subgoals.
The subproof is completed by applying H2.
Let x4 of type ι be given.
Assume H3: x4x0.
Assume H4: x3 = x1 x4.
Let x5 of type ο be given.
Assume H5: ∀ x6 . and (x6x0) (x1 x6 = x3)x5.
Apply H5 with x4.
Apply andI with x4x0, x1 x4 = x3 leaving 2 subgoals.
The subproof is completed by applying H3.
Let x6 of type ιιο be given.
The subproof is completed by applying H4 with λ x7 x8 . x6 x8 x7.