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 be given.
Let x5 of type ι be given.
Apply unknownprop_f7ba923a48e879b1ae29842e5381780ef855848ef1312b826f3310a937c24959 with
5f5a0.. 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_a24d00d7d58489d5e03d60c0e95229905bfc68c6753101dbb87b43d46b7bffe2 with x0, x2, x4.
Apply and3I with
x0 = x1,
∀ x6 . prim1 x6 x0 ⟶ x2 x6 = x3 x6,
x4 = x5 leaving 3 subgoals.
The subproof is completed by applying L2.
Let x6 of type ι be given.
Apply unknownprop_40730fb0a004b91a28776735d67465e69576d851dd9fd3b6f48aaa88954c688b 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_40730fb0a004b91a28776735d67465e69576d851dd9fd3b6f48aaa88954c688b with
x1,
x3,
x5,
x6,
λ x8 x9 : ο . x7 x9 x8.
The subproof is completed by applying L4.
Apply unknownprop_e800aee987e9a3dc43bc88979595ea06431689cd684eb2e3aa9b1f10aef3d05c 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_e800aee987e9a3dc43bc88979595ea06431689cd684eb2e3aa9b1f10aef3d05c with x1, x3, x5, λ x7 x8 . x6 x8 x7.