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Proof step 2 from proof perm-ins (previous step)

perm((x + ins≤(a, y)) -1l a, x + y) ⊦ perm((x + ins≤(a, y)) -1l a, z) ↔ perm(x + y, z)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
perm((x + ins≤(a, y)) -1l a, x + y), perm(x + y, (x + ins≤(a, y)) -1l a) ⊦ perm((x + ins≤(a, y)) -1l a, z) ↔ perm(x + y, z)

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ perm(x + y, x + z) ↔ perm(y, z); (s)% ⊦ perm(x, x); (s)%trans: ⊦ perm(x, y) ∧ perm(y, z) → perm(x, z); (forward) from specification list-perm%sym-01: ⊦ perm(x, y) → perm(y, x); (forward) from specification list-perm