Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι → ι → ι be given.
Let x4 of type ι → ι → ι be given.
Let x5 of type ι → ι → ο be given.
Let x6 of type ι → ι → ι be given.
Assume H1:
∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ x6 x7 x8 = x6 x9 x10 ⟶ and (x7 = x9) (x8 = x10).
Apply unknownprop_af2166d697755da1827fc2a3c0d003885ac9c529b0f3fc6fddf0106420f58ed1 with
x0,
x1,
x2,
x3,
x4,
x5,
x6 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply unknownprop_3708d5c1640864f559aea4941df624e8a0d1857c9693dab1782666e048041e6c with
x0,
x1,
x2,
x3,
x4,
x5,
x6 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply unknownprop_b278b789db66f678b54898c9c9fba6f986aaf8de4c43dd4b8d57bcc8f68f8f0d with
x0,
x1,
x2,
x3,
x4,
x5,
x6 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply unknownprop_4e74e812ee4eac7759fc536e7c256db03507d970f402c23c5f413e32124ec946 with
x0,
x1,
x2,
x3,
x4,
x5,
x6 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.