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.
Apply unknownprop_92c6fa644c6dced27956132c489750908a0c8c60a2c0fd4eb67751c9bc54bfc0 with
x1,
x3.
The subproof is completed by applying H0.
Let x4 of type ι → ι → ι be given.
Assume H3:
∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x3 x5 x6 = x4 x5 x6.
Apply unknownprop_06a0863c52a798b296710f9b55d879996a1cdd0acf5946530e14484efc5546c2 with
x0,
x1,
x2,
x3,
λ x5 x6 : ο . 93c99.. (987b2.. x0 x2) (λ x7 . λ x8 : ι → ι → ι . a0fbb.. x1 x4 x7) = x6.
Apply unknownprop_06a0863c52a798b296710f9b55d879996a1cdd0acf5946530e14484efc5546c2 with
x0,
x1,
x2,
x4,
λ x5 x6 : ο . x6 = a0fbb.. x1 x3 x0.
Let x5 of type ο → ο → ο be given.
Apply unknownprop_b87031dd7338a4279e9f1a76b9b31c03388ac0ad439d53bccbbb4f7b2ef357c1 with
x0,
x1,
x3,
x4,
λ x6 x7 : ο . x5 x7 x6 leaving 3 subgoals.
The subproof is completed by applying L2.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
Apply unknownprop_90e0281ca50dd9937c4dc4598e4b18b763eeb528d21427cfd7d571699b566522 with
λ x4 . λ x5 : ι → ι → ι . 93c99.. (987b2.. x0 x2) (λ x6 . λ x7 : ι → ι → ι . a0fbb.. x4 x5 x6),
x1,
x3,
λ x4 x5 : ο . x5 = a0fbb.. x1 x3 x0 leaving 2 subgoals.
The subproof is completed by applying L3.
The subproof is completed by applying unknownprop_06a0863c52a798b296710f9b55d879996a1cdd0acf5946530e14484efc5546c2 with x0, x1, x2, x3.