Apply unknownprop_b35032c81ea06ad673f8a0490d5be4e7b984453ec9378fed4adde429c2b88d75 with
λ x0 . (x0 = 1 ⟶ ∀ x1 : ο . x1) ⟶ ∀ x1 . x1 ∈ x0 ⟶ ordsucc (mul_nat x1 x1) ∈ mul_nat x0 x0 leaving 3 subgoals.
Assume H0: 0 = 1 ⟶ ∀ x0 : ο . x0.
Let x0 of type ι be given.
Assume H1: x0 ∈ 0.
Apply FalseE with
ordsucc (mul_nat x0 x0) ∈ mul_nat 0 0.
Apply EmptyE with
x0.
The subproof is completed by applying H1.
Assume H0: 1 = 1 ⟶ ∀ x0 : ο . x0.
Apply FalseE with
∀ x0 . x0 ∈ 1 ⟶ ordsucc (mul_nat x0 x0) ∈ mul_nat 1 1.
Apply H0.
set y0 to be 1
Let x1 of type ι → ι → ο be given.
Assume H1: x1 y0 y0.
The subproof is completed by applying H1.
Let x0 of type ι be given.
Apply unknownprop_ee483e984383f366e689b78ef1dc2c6d11e7826cb759a224618f578d3e31046b with
x0.
The subproof is completed by applying H0.