Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type (ι → ο) → ο be given.
Let x3 of type (ι → ο) → ο be given.
Apply unknownprop_4418ace6d5c20f38cadb4d9e1d3d8f5879244a6578517e16de54bd58b60c0e1a with
35104.. x0 x2,
x1,
x3.
The subproof is completed by applying H0.
Claim L2: x0 = x1
Apply L1 with
λ x4 x5 . x0 = x5.
The subproof is completed by applying unknownprop_73cbfbefa0026020cb29acf19575c6895e982d80894689a2eefd5ca0f4010f05 with x0, x2.
Apply andI with
x0 = x1,
∀ x4 : ι → ο . (∀ x5 . x4 x5 ⟶ prim1 x5 x0) ⟶ x2 x4 = x3 x4 leaving 2 subgoals.
The subproof is completed by applying L2.
Let x4 of type ι → ο be given.
Assume H3:
∀ x5 . x4 x5 ⟶ prim1 x5 x0.
Claim L4:
∀ x5 . x4 x5 ⟶ prim1 x5 x1Apply L2 with
λ x5 x6 . ∀ x7 . x4 x7 ⟶ prim1 x7 x5.
The subproof is completed by applying H3.
Apply unknownprop_a43e2c960a060cf2cbb41d55511fc48d292b3f138aadca7f276be3ed64c8fb26 with
x0,
x2,
x4,
λ x5 x6 : ο . x6 = x3 x4 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply H0 with
λ x5 x6 . decode_c (f482f.. x6 (4ae4a.. 4a7ef..)) x4 = x3 x4.
Let x5 of type ο → ο → ο be given.
Apply unknownprop_a43e2c960a060cf2cbb41d55511fc48d292b3f138aadca7f276be3ed64c8fb26 with
x1,
x3,
x4,
λ x6 x7 : ο . x5 x7 x6.
The subproof is completed by applying L4.