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Proof step 1 from proof app-03 (conclusion)

⊦ perm(x, x + y) ↔ y = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ (∀ a. #oc(a, y) = 0) ↔ y = []

Rule argument

Additional information

Used simplifier rules: perm-def: ⊦ perm(x, y) ↔ ¬ ¬(x ⊆m y ∧ y ⊆m x);%msubset: ⊦ x ⊆m y ↔ (∀ a. #oc(a, x) ≤ #oc(a, y));%ocappend: ⊦ #oc(a, x + y) = #oc(a, x) + #oc(a, y);%lep-01: ⊦ m + n ≤ m ↔ n = 0; from specification nat%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%lep: ⊦ m ≤ m + n; from specification nat%a: ⊦ (x + y) + z = x + y + z; from specification list