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 → ι be given.
Let x5 of type ι → ι be given.
Let x6 of type ι → ο be given.
Let x7 of type ι → ο be given.
Apply unknownprop_7bd5c275d46b9a5be91f11682f03b42077811bd33935a9a62d9979c81a223851 with
c7ccc.. x0 x2 x4 x6,
x1,
x3,
x5,
x7.
The subproof is completed by applying H0.
Claim L2: x0 = x1
Apply L1 with
λ x8 x9 . x0 = x9.
The subproof is completed by applying unknownprop_8ea88471b9883b8abffe33a1bf4f2c8ee44940148303bba54f55e7f53dcad418 with x0, x2, x4, x6.
Apply and4I with
x0 = x1,
∀ x8 : ι → ο . (∀ x9 . x8 x9 ⟶ prim1 x9 x0) ⟶ x2 x8 = x3 x8,
∀ x8 . prim1 x8 x0 ⟶ x4 x8 = x5 x8,
∀ x8 . prim1 x8 x0 ⟶ x6 x8 = x7 x8 leaving 4 subgoals.
The subproof is completed by applying L2.
Let x8 of type ι → ο be given.
Assume H3:
∀ x9 . x8 x9 ⟶ prim1 x9 x0.
Apply unknownprop_98b446a891a5eaf8b34ebae3d85a1a49a0be454d25581266db000e1a95a5a7fd with
x0,
x2,
x4,
x6,
x8,
λ x9 x10 : ο . x10 = x3 x8 leaving 2 subgoals.
The subproof is completed by applying H3.
Claim L4:
∀ x9 . x8 x9 ⟶ prim1 x9 x1Apply L2 with
λ x9 x10 . ∀ x11 . x8 x11 ⟶ prim1 x11 x9.
The subproof is completed by applying H3.
Apply H0 with
λ x9 x10 . decode_c (f482f.. x10 (4ae4a.. 4a7ef..)) x8 = x3 x8.
Let x9 of type ο → ο → ο be given.
Apply unknownprop_98b446a891a5eaf8b34ebae3d85a1a49a0be454d25581266db000e1a95a5a7fd with
x1,
x3,
x5,
x7,
x8,
λ x10 x11 : ο . x9 x11 x10.
The subproof is completed by applying L4.
Let x8 of type ι be given.
Apply unknownprop_29ae15428d4a6af9f40e9d1bd723bdbf6b510330107b33f5917ed46c37fbc7a8 with
x0,
x2,
x4,
x6,
x8,
λ x9 x10 . x10 = x5 x8 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply L2 with
λ x9 x10 . prim1 x8 x9.
The subproof is completed by applying H3.
Apply H0 with
λ x9 x10 . f482f.. (f482f.. x10 (4ae4a.. (4ae4a.. 4a7ef..))) x8 = x5 x8.
Let x9 of type ι → ι → ο be given.
Apply unknownprop_29ae15428d4a6af9f40e9d1bd723bdbf6b510330107b33f5917ed46c37fbc7a8 with
x1,
x3,
x5,
x7,
x8,
λ x10 x11 . x9 x11 x10.
The subproof is completed by applying L4.
Let x8 of type ι be given.
Apply unknownprop_3b4756d0bcc65fbb21c27a602fad093f481516dd6337133dc11f6eaeb19419b0 with
x0,
x2,
x4,
x6,
x8,
λ x9 x10 : ο . x10 = x7 x8 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply L2 with
λ x9 x10 . prim1 x8 x9.
The subproof is completed by applying H3.
Apply H0 with
λ x9 x10 . decode_p (f482f.. x10 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x8 = x7 x8.
Let x9 of type ο → ο → ο be given.
Apply unknownprop_3b4756d0bcc65fbb21c27a602fad093f481516dd6337133dc11f6eaeb19419b0 with
x1,
x3,
x5,
x7,
x8,
λ x10 x11 : ο . x9 x11 x10.
The subproof is completed by applying L4.