Let x0 of type ι be given.

Let x1 of type ι be given.

Let x2 of type ι be given.

Assume H0: gcd_reln x0 x1 x2.

Apply H0 with gcd_reln x1 x0 x2.

Assume H1: and (divides_int x2 x0) (divides_int x2 x1).

Apply H1 with (∀ x3 . divides_int x3 x0 ⟶ divides_int x3 x1 ⟶ SNoLe x3 x2) ⟶ gcd_reln x1 x0 x2.

Assume H2: divides_int x2 x0.

Assume H3: divides_int x2 x1.

Assume H4: ∀ x3 . divides_int x3 x0 ⟶ divides_int x3 x1 ⟶ SNoLe x3 x2.

Apply and3I with divides_int x2 x1, divides_int x2 x0, ∀ x3 . divides_int x3 x1 ⟶ divides_int x3 x0 ⟶ SNoLe x3 x2 leaving 3 subgoals.

The subproof is completed by applying H3.

The subproof is completed by applying H2.

Let x3 of type ι be given.

Assume H5: divides_int x3 x1.

Assume H6: divides_int x3 x0.

Apply H4 with x3 leaving 2 subgoals.

The subproof is completed by applying H6.

The subproof is completed by applying H5.

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Proofgold Proof