Let x0 of type ι be given.
Let x1 of type ι be given.
Apply H0 with
divides_int_alt1 x0 x1.
Apply H1 with
(∃ x2 . and (x2 ∈ omega) (mul_nat x0 x2 = x1)) ⟶ divides_int_alt1 x0 x1.
Assume H2:
x0 ∈ omega.
Assume H3:
x1 ∈ omega.
Apply and3I with
x0 ∈ int_alt1,
x1 ∈ int_alt1,
∃ x2 . and (x2 ∈ int_alt1) (mul_SNo x0 x2 = x1) leaving 3 subgoals.
Apply unknownprop_c213ff287d87049b1e6a47a232f87c366800922741a9eeadb1d3ac2fbadaf052 with
x0.
The subproof is completed by applying H2.
Apply unknownprop_c213ff287d87049b1e6a47a232f87c366800922741a9eeadb1d3ac2fbadaf052 with
x1.
The subproof is completed by applying H3.
Apply H4 with
∃ x2 . and (x2 ∈ int_alt1) (mul_SNo x0 x2 = x1).
Let x2 of type ι be given.
Apply H5 with
∃ x3 . and (x3 ∈ int_alt1) (mul_SNo x0 x3 = x1).
Assume H6:
x2 ∈ omega.
Let x3 of type ο be given.
Apply H8 with
x2.
Apply andI with
x2 ∈ int_alt1,
mul_SNo x0 x2 = x1 leaving 2 subgoals.
Apply unknownprop_c213ff287d87049b1e6a47a232f87c366800922741a9eeadb1d3ac2fbadaf052 with
x2.
The subproof is completed by applying H6.
Apply mul_nat_mul_SNo with
x0,
x2,
λ x4 x5 . x4 = x1 leaving 3 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H6.
The subproof is completed by applying H7.