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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: coprime_nat x0 x1.
Apply H0 with 76fc5.. x0 x1.
Assume H1: and (x0 ∈ omega) (x1 ∈ omega).
Apply H1 with (∀ x2 . x2 ∈ setminus omega 1 ⟶ divides_nat x2 x0 ⟶ divides_nat x2 x1 ⟶ x2 = 1) ⟶ 76fc5.. x0 x1.
Assume H2: x0 ∈ omega.
Assume H3: x1 ∈ omega.
Assume H4: ∀ x2 . x2 ∈ setminus omega 1 ⟶ divides_nat x2 x0 ⟶ divides_nat x2 x1 ⟶ x2 = 1.
Apply and3I with x0 ∈ int_alt1, x1 ∈ int_alt1, ∀ x2 . x2 ∈ setminus omega 1 ⟶ divides_int_alt1 x2 x0 ⟶ divides_int_alt1 x2 x1 ⟶ x2 = 1 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.
Let x2 of type ι be given.
Assume H5: x2 ∈ setminus omega 1.
Assume H6: divides_int_alt1 x2 x0.
Assume H7: divides_int_alt1 x2 x1.
Claim L8: x2 ∈ omega
Apply setminusE1 with omega, 1, x2.
The subproof is completed by applying H5.
Apply H4 with x2 leaving 3 subgoals.
The subproof is completed by applying H5.
Apply unknownprop_c9c36883e1bc2d8bed3fd5dc85072c7e932e4427b6b65effb58ba8e6a414fb93 with x2, x0 leaving 3 subgoals.
The subproof is completed by applying L8.
The subproof is completed by applying H2.
The subproof is completed by applying H6.
Apply unknownprop_c9c36883e1bc2d8bed3fd5dc85072c7e932e4427b6b65effb58ba8e6a414fb93 with x2, x1 leaving 3 subgoals.
The subproof is completed by applying L8.
The subproof is completed by applying H3.
The subproof is completed by applying H7.
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