Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι → ο be given.
Apply CSNo_Im1 with
SNo_pair x0 x1,
x1 = CSNo_Im (SNo_pair x0 x1),
λ x3 x4 . x2 x4 x3 leaving 2 subgoals.
Apply CSNo_I with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply CSNo_Re2 with
x0,
x1,
λ x3 x4 . SNo_pair x0 x1 = SNo_pair x4 (CSNo_Im (SNo_pair x0 x1)) ⟶ x1 = CSNo_Im (SNo_pair x0 x1) leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply SNo_pair_prop_2 with
x0,
x1,
x0,
CSNo_Im (SNo_pair x0 x1) leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
The subproof is completed by applying H3.