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Proof step 23 from proof perm-put-del1 (previous step)

n < # y, a ∈ y ⊦ #oc(a, y[n, a] -1l a) = #oc(a, y), a = y[n], y = []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: del1 seq: ⊦ a ∈ x → #oc(a, x -1l a) = #oc(a, x) -1 subst: [x, a] → [y[n, a], a] flags: <all paths>

Additional information

Used simplifier rules: notin: ⊦ ¬ a ∈ x → #oc(a, x) = 0;%in-05: ⊦ a ∈ x → #oc(a, x) ≠ 0;%ocs-put: ⊦ x[m] ≠ a ∧ m < # x → #oc(a, x[m, a]) = #oc(a, x) + 1;% ⊦ (m + 1)-1 = m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ ¬ a ∈ x → x -1l a = x; (s)% ⊦ a ≠ x[m] ∧ m < # x → (a ∈ x[m, b] ↔ a = b ∨ a ∈ x); (ws) Used terms: y[n, a], a