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

n0 + 1 ≠ 0, perm(x, a + mklist(a, n0 + 1 - 1)), perm(a + mklist(a, n0 + 1 - 1), x), ∀ x0, a0. perm(x0, mklist(a0, n0)) → x0 = mklist(a0, n0) ⊦ x = a + mklist(a, n0 + 1 - 1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
perm(x -1l a, mklist(a, n0)), perm(mklist(a, n0), x -1l a), a ∈ x, ∀ x0, a0. perm(x0, mklist(a0, n0)) → x0 = mklist(a0, n0) ⊦ x = a ' + mklist(a, n0)

Rule argument

Additional information

Used simplifier rules: del: ⊦ perm(x, a ' + y) ↔ a ∈ x ∧ perm(x -1l a, y);%perm-l: ⊦ perm(a ' + x, y) ↔ a ∈ y ∧ perm(x, y -1l a);%trans: ⊦ perm(x, y) ∧ perm(y, z) → perm(x, z);%sym-01: ⊦ perm(x, y) → perm(y, x);%ref: ⊦ perm(x, x);%a: ⊦ (x + y) + z = x + y + z; from specification list%oz: ⊦ m + 1 ≠ 0; from specification nat-basic2%c: ⊦ a + x = a ' + x; from specification list%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%add-base: ⊦ n + 0 = n; from specification nat-basic2%add-01: ⊦ n ≤ m → m + n0 - n = (m - n) + n0; from specification nat