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Proof step 1 from proof subrec-01 (conclusion)

⊦ x ⊆m a ' + y ↔ #oc(a, x) ≤ #oc(a, y) + 1 ∧ x -1l a ⊆m y

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ a, y. x0 ⊆m a ' + y ↔ #oc(a, x0) ≤ #oc(a, y) + 1 ∧ x0 -1l a ⊆m y ⊦ a0 + x0 ⊆m a ' + y ↔ #oc(a, a0 + x0) ≤ #oc(a, y) + 1 ∧ (a0 + x0) -1l a ⊆m y

Rule argument

term: x

Additional information

Used simplifier rules: subempty: ⊦ [] ⊆m x;%oc-e: ⊦ #oc(a, []) = 0;%list freely generated by [], +;;%lez: ⊦ 0 ≤ m; from specification nat%del1-e: ⊦ [] -1l a = []; from specification list-del