Let x0 of type ι → ι → ο be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Assume H1: x0 x1 x2.
Claim L2: x0 x1 = x0 x2
Apply pred_ext_2 with
x0 x1,
x0 x2 leaving 2 subgoals.
Let x3 of type ι be given.
Assume H2: x0 x1 x3.
Apply per_stra1 with
x0,
x2,
x1,
x3 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Let x3 of type ι be given.
Assume H2: x0 x2 x3.
Apply per_tra with
x0,
x1,
x2,
x3 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply L2 with
λ x3 x4 : ι → ο . prim0 (x0 x1) = prim0 x3.
Let x3 of type ι → ι → ο be given.
The subproof is completed by applying H3.