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Proof step 4 from proof subdel-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: notin: ⊦ ¬ a ∈ x → #oc(a, x) = 0;%in-05: ⊦ a ∈ x → #oc(a, x) ≠ 0;%pred-03: ⊦ n -1 = n - 1; from specification nat%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat%one-01: ⊦ m < 1 ↔ m = 0; from specification nat-basic1%ls-03: n0 ≤ n ⊦ n - n0 ≤ m ↔ n ≤ m + n0; from specification nat%in-02-01: ⊦ ¬ a ∈ x → x -1l a = x; from specification list-del%lez: ⊦ 0 ≤ m; from specification nat Used terms: x, a