Proofgold Proof

pf

Let x0 of type ι → ι → ο be given.

Assume H0: and (symmetric x0) (transitive x0).

Let x1 of type ι be given.

Let x2 of type ι be given.

Let x3 of type ι be given.

Assume H1: x0 x2 x1.

Assume H2: x0 x3 x2.

Apply H0 with x0 x1 x3.

Assume H3: symmetric x0.

Assume H4: transitive x0.

Apply H3 with x3, x1.

Apply H4 with x3, x2, x1 leaving 2 subgoals.

The subproof is completed by applying H2.

The subproof is completed by applying H1.

■