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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: SNo x0.
Assume H1: SNo x1.
Apply CSNo_Re1 with SNo_pair x0 x1, CSNo_Re (SNo_pair x0 x1) = x0 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.
Assume H2: SNo (CSNo_Re (SNo_pair x0 x1)).
Assume H3: ∃ x2 . and (SNo x2) (SNo_pair x0 x1 = SNo_pair (CSNo_Re (SNo_pair x0 x1)) x2).
Apply H3 with CSNo_Re (SNo_pair x0 x1) = x0.
Let x2 of type ι be given.
Assume H4: (λ x3 . and (SNo x3) (SNo_pair x0 x1 = SNo_pair (CSNo_Re (SNo_pair x0 x1)) x3)) x2.
Apply H4 with CSNo_Re (SNo_pair x0 x1) = x0.
Assume H5: SNo x2.
Assume H6: SNo_pair x0 x1 = SNo_pair (CSNo_Re (SNo_pair x0 x1)) x2.
Let x3 of type ι → ι → ο be given.
Apply SNo_pair_prop_1 with x0, x1, CSNo_Re (SNo_pair x0 x1), x2, λ x4 x5 . x3 x5 x4 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
The subproof is completed by applying H6.
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