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.
Apply unknownprop_a2011094301afc7191f07da5aaff5089e647cc16d8e3ddd255f80564fc54c630 with
81bb1.. x0 x2,
x1,
x3.
The subproof is completed by applying H0.
Claim L2: x0 = x1
Apply L1 with
λ x4 x5 . x0 = x5.
The subproof is completed by applying unknownprop_5ac7e58347fbd821fb6c06fd77c373ba625105663e23fa511d1e2827eb3c4615 with x0, x2.
Apply andI with
x0 = x1,
∀ x4 . prim1 x4 x0 ⟶ x2 x4 = x3 x4 leaving 2 subgoals.
The subproof is completed by applying L2.
Let x4 of type ι be given.
Apply L2 with
λ x5 x6 . prim1 x4 x5.
The subproof is completed by applying H3.
Apply unknownprop_12d3c711d3bd2930236f54800b174e3b630cb0c252b0ae281ac1e81b5d03da83 with
x0,
x2,
x4,
λ x5 x6 : ο . x6 = x3 x4 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply H0 with
λ x5 x6 . decode_p (f482f.. x6 (4ae4a.. 4a7ef..)) x4 = x3 x4.
Let x5 of type ο → ο → ο be given.
Apply unknownprop_12d3c711d3bd2930236f54800b174e3b630cb0c252b0ae281ac1e81b5d03da83 with
x1,
x3,
x4,
λ x6 x7 : ο . x5 x7 x6.
The subproof is completed by applying L4.