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

∀ x, a. perm(x, mklist(a, n0)) ↔ x = mklist(a, n0) ⊦ perm(x, mklist(a, n0 +1)) ↔ x = mklist(a, n0 +1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
perm(x, mklist(a, n0 + 1)), perm(mklist(a, n0 + 1), x), ∀ x0, a0. perm(x0, mklist(a0, n0)) → x0 = mklist(a0, n0) ⊦ x = mklist(a, n0 + 1)

Rule argument

Additional information

Used simplifier rules: ref: ⊦ perm(x, x);%sym-01: ⊦ perm(x, y) → perm(y, x);%trans: ⊦ perm(x, y) ∧ perm(y, z) → perm(x, z);%succ: ⊦ m +1 = m + 1; from specification nat-basic2