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Proof step 5 from proof perm-ins (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ perm(x, y) → (perm(x -1l a, z) ↔ perm(y -1l a, z))
Proof step 7:
perm(x + ins≤(a, y), ins≤(a, y) + x) ⊦ perm((x + ins≤(a, y)) -1l a, z) ↔ perm(x + y, z), perm(x + y, (x + ins≤(a, y)) -1l a), perm((ins≤(a, y) + x) -1l a, x + y)

Rule argument

spec: list-perm inst: name: perm-del seq: ⊦ perm(x, y) → (perm(x -1l a, z) ↔ perm(y -1l a, z)) subst: [x, y, a, z] → [x + ins≤(a, y), ins≤(a, y) + x, a, x + y] flags: rewrite

Additional information

Used simplifier rules: insperm-01: ⊦ perm(ins≤(a, x), ins≤(a, y)) ↔ perm(x, y);%app-02: ⊦ perm(x + y, z + x) ↔ perm(y, z); from specification list-perm%ref: ⊦ perm(x, x); from specification list-perm%a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: x + ins≤(a, y), ins≤(a, y) + x, a, x + y