Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Let x2 of type ι → ι be given.
Assume H0:
∀ x3 . prim1 x3 x0 ⟶ x1 (x2 x3) = x3.
Apply set_ext with
94f9e.. (94f9e.. x0 (λ x3 . x2 x3)) (λ x3 . x1 x3),
x0 leaving 2 subgoals.
Let x3 of type ι be given.
Apply unknownprop_d908b89102f7b662c739e5a844f67efc8ae1cd05a2e9ce1e3546fa3885f40100 with
94f9e.. x0 (λ x4 . x2 x4),
x1,
x3,
prim1 x3 x0 leaving 2 subgoals.
The subproof is completed by applying H1.
Let x4 of type ι be given.
Assume H3: x3 = x1 x4.
Apply unknownprop_d908b89102f7b662c739e5a844f67efc8ae1cd05a2e9ce1e3546fa3885f40100 with
x0,
x2,
x4,
prim1 x3 x0 leaving 2 subgoals.
The subproof is completed by applying H2.
Let x5 of type ι be given.
Assume H5: x4 = x2 x5.
Apply H3 with
λ x6 x7 . prim1 x7 x0.
Apply H5 with
λ x6 x7 . prim1 (x1 x7) x0.
Apply H0 with
x5,
λ x6 x7 . prim1 x7 x0 leaving 2 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H4.
Let x3 of type ι be given.
Apply H0 with
x3,
λ x4 x5 . prim1 x4 (94f9e.. (94f9e.. x0 x2) x1) leaving 2 subgoals.
The subproof is completed by applying H1.
Apply unknownprop_4785a7374559bd7d78314ce01f76cab97234c9b29cfa5b01c939c64f8ccf18e4 with
94f9e.. x0 (λ x4 . x2 x4),
x1,
x2 x3.
Apply unknownprop_4785a7374559bd7d78314ce01f76cab97234c9b29cfa5b01c939c64f8ccf18e4 with
x0,
x2,
x3.
The subproof is completed by applying H1.