Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι be given.
Let x3 of type ι → ι be given.
Apply H0 with
c2e41.. x0 x1.
Assume H3:
∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ x2 x4 = x2 x5 ⟶ x4 = x5.
Apply H1 with
c2e41.. x0 x1.
Assume H5:
∀ x4 . prim1 x4 x1 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x3 x4 = x3 x5 ⟶ x4 = x5.
Apply unknownprop_1c03dbc8933f14179c6d1fab30498a3d9cfe087cf19262a1a909f1f505467ff7 with
x0,
λ x4 . 94f9e.. (1ad11.. x1 (94f9e.. (1ad11.. x0 x4) (λ x5 . x2 x5))) (λ x5 . x3 x5),
c2e41.. x0 x1 leaving 3 subgoals.
The subproof is completed by applying L6.
The subproof is completed by applying L7.
Let x4 of type ι be given.
Apply H8 with
c2e41.. x0 x1.
Apply unknownprop_4865425a7f56150b37062def658749568c73ac3811495e4e2624803c98cf736b with
x0,
x1,
λ x5 . If_i (prim1 x5 x4) (inv x1 x3 x5) (x2 x5).
Apply and3I with
∀ x5 . prim1 x5 x0 ⟶ prim1 ((λ x6 . If_i (prim1 x6 x4) (inv x1 x3 x6) (x2 x6)) x5) x1,
∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ (λ x7 . If_i (prim1 x7 x4) (inv x1 x3 x7) (x2 x7)) x5 = (λ x7 . If_i (prim1 x7 x4) (inv x1 x3 x7) (x2 x7)) x6 ⟶ x5 = x6,
∀ x5 . prim1 x5 x1 ⟶ ∃ x6 . and (prim1 x6 x0) ((λ x7 . If_i (prim1 x7 x4) (inv x1 x3 x7) (x2 x7)) x6 = x5) leaving 3 subgoals.
Let x5 of type ι be given.
Apply xm with
prim1 x5 x4,
prim1 (If_i (prim1 x5 x4) (inv x1 x3 x5) (x2 x5)) x1 leaving 2 subgoals.
Apply If_i_1 with
prim1 x5 x4,
inv x1 x3 x5,
x2 x5,
λ x6 x7 . prim1 x7 x1 leaving 2 subgoals.
The subproof is completed by applying H12.
Apply unknownprop_d908b89102f7b662c739e5a844f67efc8ae1cd05a2e9ce1e3546fa3885f40100 with
1ad11.. x1 (94f9e.. ... ...),
...,
...,
... leaving 2 subgoals.