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Proof step 5 from proof perm-del-01 (previous step)

perm(x -l a, z), perm(x, y), perm(z, x -l a), perm(y, x), a0 ∈ y -l a ∨ a0 ∈ z ⊦ #oc(a0, y -l a) = #oc(a0, z)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ a ≠ b → #oc(a, x -l b) = #oc(a, x)
Proof step 7:
a0 ≠ a, perm(x -l a, z), perm(x, y), perm(z, x -l a), perm(y, x), a0 ∈ y -l a ∨ a0 ∈ z ⊦ #oc(a0, y) = #oc(a0, z)

Rule argument

spec: inst: name: ocs-del-length seq: ⊦ a ≠ b → #oc(a, x -l b) = #oc(a, x) subst: [b, x, a] → [a, y, a0] flags: rewrite, current

Additional information

Used simplifier rules: ocs-del: ⊦ #oc(a, x -l a) = 0;%oc-zero: ⊦ #oc(a, x) = 0 ↔ ¬ a ∈ x;%perm-del-in: ⊦ a ∈ y → ¬ perm(x -l a, y); Used terms: a, y, a0