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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
perm(mklist(a, n0), x -1l a), perm(x -1l a, mklist(a, n0)), 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);%del-01: ⊦ 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% ⊦ m + 1 ≠ 0; (s)% ⊦ a + x = a ' + x; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ n ≤ m → m + n0 - n = (m - n) + n0; (s)