Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι → ι be given.
Let x3 of type ι → ι → ι be given.
Assume H2:
∀ x4 . prim1 x4 x1 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x2 x4 x5 = x3 x4 x5.
Let x4 of type ι be given.
Let x5 of type ι be given.
Apply unknownprop_d908b89102f7b662c739e5a844f67efc8ae1cd05a2e9ce1e3546fa3885f40100 with
x0,
λ x6 . x3 x4 (x3 x6 (explicit_Group_inverse x1 x3 x4)),
x5,
prim1 x5 x0 leaving 2 subgoals.
The subproof is completed by applying H5.
Let x6 of type ι be given.
Apply H7 with
λ x7 x8 . x8 = x2 x4 (x2 x6 (explicit_Group_inverse x1 x2 x4)).
Apply L8 with
λ x7 x8 . x3 x4 (x3 x6 x7) = x2 x4 (x2 x6 (explicit_Group_inverse x1 x2 x4)).
Apply H2 with
x6,
explicit_Group_inverse x1 x2 x4,
λ x7 x8 . x3 x4 x7 = x2 x4 (x2 x6 (explicit_Group_inverse x1 x2 x4)) leaving 3 subgoals.
Apply H1 with
x6.
The subproof is completed by applying H6.
The subproof is completed by applying L9.
Apply H2 with
x4,
x2 x6 (explicit_Group_inverse x1 x2 x4),
λ x7 x8 . x7 = x2 x4 (x2 x6 (explicit_Group_inverse x1 x2 x4)) leaving 3 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying L10.
Let x7 of type ι → ι → ο be given.
The subproof is completed by applying H11.
Apply H3 with
x4,
x5 leaving 2 subgoals.
The subproof is completed by applying H4.
Apply L11 with
λ x7 x8 . prim1 x8 (94f9e.. x0 (λ x9 . x2 x4 (x2 x9 (explicit_Group_inverse x1 x2 x4)))).
Apply unknownprop_4785a7374559bd7d78314ce01f76cab97234c9b29cfa5b01c939c64f8ccf18e4 with
x0,
λ x7 . x2 x4 (x2 x7 (explicit_Group_inverse x1 x2 x4)),
x6.
The subproof is completed by applying H6.