Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ο be given.
Let x3 of type ι → ο be given.
Let x4 of type ι → ο be given.
Let x5 of type ι → ο be given.
Apply unknownprop_46dd056036474c70cd94c7da1bc25abbf50dcb41b86cab7424c380fe7ecbda9d with
2c81e.. 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_5a3da60961dc828c3b054c11b04e3fdd5c1744838c2dc7756fea2affd3e32f1d with x0, x2, x4.
Apply and3I with
x0 = x1,
∀ x6 . prim1 x6 x0 ⟶ x2 x6 = x3 x6,
∀ x6 . prim1 x6 x0 ⟶ x4 x6 = x5 x6 leaving 3 subgoals.
The subproof is completed by applying L2.
Let x6 of type ι be given.
Apply unknownprop_f89b2eb83b1375e36cd0ad303ce6605f299e4461f16d1e3558e0856c6ba04a59 with
x0,
x2,
x4,
x6,
λ x7 x8 : ο . x8 = x3 x6 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply L2 with
λ x7 x8 . prim1 x6 x7.
The subproof is completed by applying H3.
Apply H0 with
λ x7 x8 . decode_p (f482f.. x8 (4ae4a.. 4a7ef..)) x6 = x3 x6.
Let x7 of type ο → ο → ο be given.
Apply unknownprop_f89b2eb83b1375e36cd0ad303ce6605f299e4461f16d1e3558e0856c6ba04a59 with
x1,
x3,
x5,
x6,
λ x8 x9 : ο . x7 x9 x8.
The subproof is completed by applying L4.
Let x6 of type ι be given.
Apply unknownprop_353e1ebd952cdfa03484f2eb926c90f10068fbb8a5e3cf11a3a5f72589e7c77c with
x0,
x2,
x4,
x6,
λ x7 x8 : ο . x8 = x5 x6 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply L2 with
λ x7 x8 . prim1 x6 x7.
The subproof is completed by applying H3.
Apply H0 with
λ x7 x8 . decode_p (f482f.. x8 (4ae4a.. (4ae4a.. 4a7ef..))) x6 = x5 x6.
Let x7 of type ο → ο → ο be given.
Apply unknownprop_353e1ebd952cdfa03484f2eb926c90f10068fbb8a5e3cf11a3a5f72589e7c77c with
x1,
x3,
x5,
x6,
λ x8 x9 : ο . x7 x9 x8.
The subproof is completed by applying L4.