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Proof step 9 from proof perm-put-del1 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ a ∈ x → #oc(a, x -1l a) = #oc(a, x) -1
Proof step 11:
n < # y, y[n] ∈ y, y[n] ∈ y[n, a] -1l a ∨ y[n] ∈ y -1l y[n] ⊦ #oc(y[n], y[n, a] -1l a) = #oc(y[n], y) -1, y = []

Rule argument

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

Additional information

Used simplifier rules: notin: ⊦ ¬ a ∈ x → #oc(a, x) = 0;%oc-zero: ⊦ #oc(a, x) = 0 ↔ ¬ a ∈ x;% ⊦ ¬ a ∈ x → x -1l a = x; (s)% ⊦ m < # x → (x[m] ∈ x ↔ true); (ss) Used terms: y, y[n]