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Proof step 4 from proof oc-del-01 (previous step)

#oc(a, x) + #oc(a, y) = m + 1, a ∈ y ⊦ #oc(a, (x + y) -1l a) = m

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-perm inst: name: del1 seq: ⊦ a ∈ x → #oc(a, x -1l a) = #oc(a, x) -1 subst: [x, a] → [x + y, a] flags: rewrite, current

Additional information

Used simplifier rules: ocappend: ⊦ #oc(a, x + y) = #oc(a, x) + #oc(a, y);%ocappend: ⊦ #oc(a, x + y) = #oc(a, x) + #oc(a, y);%a: ⊦ (x + y) + z = x + y + z; from specification list%pred-03: ⊦ n -1 = n - 1; from specification nat%in-12: ⊦ a ∈ y → a ∈ x + y; from specification list%add-01: ⊦ n ≤ m → m + n0 - n = (m - n) + n0; from specification nat%add-base: ⊦ n + 0 = n; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%in-02-01: ⊦ ¬ a ∈ x → x -1l a = x; from specification list-del Used terms: x + y, a