Let x0 of type ι be given.
Apply nat_ind with
λ x1 . even_nat (mul_nat x0 x1) leaving 2 subgoals.
Apply mul_nat_0R with
x0,
λ x1 x2 . even_nat x2.
The subproof is completed by applying even_nat_0.
Let x1 of type ι be given.
Apply mul_nat_SR with
x0,
x1,
λ x2 x3 . even_nat x3 leaving 2 subgoals.
The subproof is completed by applying H1.
Apply unknownprop_209520ddb6996883d29652b83315cacb601bd4047ab755a61e6bc2c1bd94b0c5 with
x0,
mul_nat x0 x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.