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Proof step 3 from proof insperm-01 (previous step)

perm(a ' + x, ins≤(a, x)) ⊦ perm(ins≤(a, x), ins≤(a, y)) ↔ perm(x, y)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
perm(a ' + x, ins≤(a, x)), perm(ins≤(a, x), a ' + x) ⊦ perm(ins≤(a, x), ins≤(a, y)) ↔ perm(x, y)

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ perm(x, x); (s)% ⊦ perm(x + y, x + z) ↔ perm(y, z); (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