Let x0 of type ι be given.
Let x1 of type ι be given.
Apply setminusE with
omega,
1,
x0,
mul_nat x0 x0 = mul_nat 2 (mul_nat x1 x1) ⟶ ∀ x2 : ο . x2 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply setminusE with
omega,
1,
x1,
mul_nat x0 x0 = mul_nat 2 (mul_nat x1 x1) ⟶ ∀ x2 : ο . x2 leaving 2 subgoals.
The subproof is completed by applying H1.
Claim L7: x1 = 0
Apply form100_1_v1_lem with
x0,
x1 leaving 3 subgoals.
Apply omega_nat_p with
x0.
The subproof is completed by applying H2.
Apply omega_nat_p with
x1.
The subproof is completed by applying H4.
The subproof is completed by applying H6.
Apply H5.
Apply L7 with
λ x2 x3 . x3 ∈ 1.
The subproof is completed by applying In_0_1.