Let x0 of type ι be given.
Let x1 of type ι be given.
Apply H0 with
even_nat (add_SNo x0 x1).
Assume H3:
∀ x2 . x2 ∈ omega ⟶ x0 = mul_nat 2 x2 ⟶ ∀ x3 : ο . x3.
Apply H1 with
even_nat (add_SNo x0 x1).
Assume H5:
∀ x2 . x2 ∈ omega ⟶ x1 = mul_nat 2 x2 ⟶ ∀ x3 : ο . x3.
Apply add_nat_add_SNo with
x0,
x1,
λ x2 x3 . even_nat x2 leaving 3 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H4.
Apply unknownprop_d79d4f48cc8316d2cfd7d64249eea9eca38257f800721e161e9a4245bd603310 with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.