Let x0 of type ι → ((ι → ο) → ο) → ι → ι be given.
Let x1 of type ι be given.
Let x2 of type (ι → ο) → ο be given.
Let x3 of type ι be given.
Assume H0:
∀ x4 : (ι → ο) → ο . (∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x1) ⟶ iff (x2 x5) (x4 x5)) ⟶ x0 x1 x4 x3 = x0 x1 x2 x3.
Apply unknownprop_0f0f5ff3472b5b4a811d9c6a1bfb2a230ff6b344f362350f75d2ec4bedc64cd9 with
x1,
x2,
x3,
λ x4 x5 . x0 x4 (decode_c (f482f.. (71057.. x1 x2 x3) (4ae4a.. 4a7ef..))) (f482f.. (71057.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) = x0 x1 x2 x3.
Apply unknownprop_f4e8077962fd33ae98b12c23ffaa6efc03c87be0d8acc10bbfb19835aabc4441 with
x1,
x2,
x3,
λ x4 x5 . x0 x1 (decode_c (f482f.. (71057.. x1 x2 x3) (4ae4a.. 4a7ef..))) x4 = x0 x1 x2 x3.
Apply H0 with
decode_c (f482f.. (71057.. x1 x2 x3) (4ae4a.. 4a7ef..)).
Let x4 of type ι → ο be given.
Assume H1:
∀ x5 . x4 x5 ⟶ prim1 x5 x1.
Apply unknownprop_589b5ce266c33c1f7644fa9da47798285ff9e4179a8d234a82d52953a7f67110 with
x1,
x2,
x3,
x4,
λ x5 x6 : ο . iff (x2 x4) x5 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying iff_refl with x2 x4.