Search for blocks/addresses/...

Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: atleastp x0 x1.
Let x2 of type ο be given.
Assume H1: ∀ x3 . x3x1equip x0 x3x2.
Apply H0 with x2.
Let x3 of type ιι be given.
Assume H2: inj x0 x1 x3.
Apply H2 with x2.
Assume H3: ∀ x4 . x4x0x3 x4x1.
Assume H4: ∀ x4 . x4x0∀ x5 . x5x0x3 x4 = x3 x5x4 = x5.
Apply H1 with {x3 x4|x4 ∈ x0} leaving 2 subgoals.
Let x4 of type ι be given.
Assume H5: x4prim5 x0 x3.
Apply ReplE_impred with x0, x3, x4, x4x1 leaving 2 subgoals.
The subproof is completed by applying H5.
Let x5 of type ι be given.
Assume H6: x5x0.
Assume H7: x4 = x3 x5.
Apply H7 with λ x6 x7 . x7x1.
Apply H3 with x5.
The subproof is completed by applying H6.
Let x4 of type ο be given.
Assume H5: ∀ x5 : ι → ι . bij x0 {x3 x6|x6 ∈ x0} x5x4.
Apply H5 with x3.
Apply bijI with x0, {x3 x5|x5 ∈ x0}, x3 leaving 3 subgoals.
Let x5 of type ι be given.
Assume H6: x5x0.
Apply ReplI with x0, x3, x5.
The subproof is completed by applying H6.
The subproof is completed by applying H4.
Let x5 of type ι be given.
Assume H6: x5{x3 x6|x6 ∈ x0}.
Apply ReplE_impred with x0, x3, x5, ∃ x6 . and (x6x0) (x3 x6 = x5) leaving 2 subgoals.
The subproof is completed by applying H6.
Let x6 of type ι be given.
Assume H7: x6x0.
Assume H8: x5 = x3 x6.
Let x7 of type ο be given.
Assume H9: ∀ x8 . and (x8x0) (x3 x8 = x5)x7.
Apply H9 with x6.
Apply andI with x6x0, x3 x6 = x5 leaving 2 subgoals.
The subproof is completed by applying H7.
Let x8 of type ιιο be given.
The subproof is completed by applying H8 with λ x9 x10 . x8 x10 x9.