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.
Let x4 of type ι be given.
Let x5 of type ι be given.
Apply unknownprop_604f6249a37733005212c6ef763cc1ef8c23f6bb41e288dc0decc301b50471be with
71057.. x0 x2 x4,
x1,
x3,
x5.
The subproof is completed by applying H0.
Claim L2: x0 = x1
Apply L1 with
λ x6 x7 . x0 = x7.
The subproof is completed by applying unknownprop_0f0f5ff3472b5b4a811d9c6a1bfb2a230ff6b344f362350f75d2ec4bedc64cd9 with x0, x2, x4.
Apply and3I with
x0 = x1,
∀ x6 : ι → ο . (∀ x7 . x6 x7 ⟶ prim1 x7 x0) ⟶ x2 x6 = x3 x6,
x4 = x5 leaving 3 subgoals.
The subproof is completed by applying L2.
Let x6 of type ι → ο be given.
Assume H3:
∀ x7 . x6 x7 ⟶ prim1 x7 x0.
Apply unknownprop_589b5ce266c33c1f7644fa9da47798285ff9e4179a8d234a82d52953a7f67110 with
x0,
x2,
x4,
x6,
λ x7 x8 : ο . x8 = x3 x6 leaving 2 subgoals.
The subproof is completed by applying H3.
Claim L4:
∀ x7 . x6 x7 ⟶ prim1 x7 x1Apply L2 with
λ x7 x8 . ∀ x9 . x6 x9 ⟶ prim1 x9 x7.
The subproof is completed by applying H3.
Apply H0 with
λ x7 x8 . decode_c (f482f.. x8 (4ae4a.. 4a7ef..)) x6 = x3 x6.
Let x7 of type ο → ο → ο be given.
Apply unknownprop_589b5ce266c33c1f7644fa9da47798285ff9e4179a8d234a82d52953a7f67110 with
x1,
x3,
x5,
x6,
λ x8 x9 : ο . x7 x9 x8.
The subproof is completed by applying L4.
Apply unknownprop_f4e8077962fd33ae98b12c23ffaa6efc03c87be0d8acc10bbfb19835aabc4441 with
x0,
x2,
x4,
λ x6 x7 . x7 = x5.
Apply H0 with
λ x6 x7 . f482f.. x7 (4ae4a.. (4ae4a.. 4a7ef..)) = x5.
Let x6 of type ι → ι → ο be given.
The subproof is completed by applying unknownprop_f4e8077962fd33ae98b12c23ffaa6efc03c87be0d8acc10bbfb19835aabc4441 with x1, x3, x5, λ x7 x8 . x6 x8 x7.