Apply add_SNo_cancel_L with
0,
minus_SNo 0,
0 leaving 4 subgoals.
The subproof is completed by applying SNo_0.
Apply SNo_minus_SNo with
0.
The subproof is completed by applying SNo_0.
The subproof is completed by applying SNo_0.
Claim L0: ∀ x2 : ι → ο . x2 y1 ⟶ x2 y0
Let x2 of type ι → ο be given.
Apply add_SNo_minus_SNo_rinv with
0,
λ x3 . x2 leaving 2 subgoals.
The subproof is completed by applying SNo_0.
set y3 to be λ x3 . x2
Apply add_SNo_0L with
0,
λ x4 x5 . y3 x5 x4 leaving 2 subgoals.
The subproof is completed by applying SNo_0.
The subproof is completed by applying H0.
Let x2 of type ι → ι → ο be given.
Apply L0 with
λ x3 . x2 x3 y1 ⟶ x2 y1 x3.
Assume H1: x2 y1 y1.
The subproof is completed by applying H1.