Let x0 of type ι be given.
Apply nat_ind with
λ x1 . or (x1 = 0) (x0 ⊆ mul_nat x0 x1) leaving 2 subgoals.
Apply orIL with
0 = 0,
x0 ⊆ mul_nat x0 0.
Let x1 of type ι → ι → ο be given.
Assume H1: x1 0 0.
The subproof is completed by applying H1.
Let x1 of type ι be given.
Apply orIR with
ordsucc x1 = 0,
x0 ⊆ mul_nat x0 (ordsucc x1).
Apply mul_nat_SR with
x0,
x1,
λ x2 x3 . x0 ⊆ x3 leaving 2 subgoals.
The subproof is completed by applying H1.
Apply unknownprop_2dcf4dd8557a0ffd2a187961d1bc330ef1aae42c546555814bac26eb5e3c6d68 with
x0,
mul_nat x0 x1.
Apply mul_nat_p with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.