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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

Proof step 5:
⊦ a ∈ x → #oc(a, x -1l a) = #oc(a, x) -1

Rule argument

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

Additional information

Used simplifier rules: notin: ⊦ ¬ a ∈ x → #oc(a, x) = 0;%in-05: ⊦ a ∈ x → #oc(a, x) ≠ 0;% ⊦ n -1 = n - 1; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < 1 ↔ m = 0; (s)%n0 ≤ n ⊦ n - n0 ≤ m ↔ n ≤ m + n0; (s)% ⊦ ¬ a ∈ x → x -1l a = x; (s)% ⊦ 0 ≤ m; (s) Used terms: x, a