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Proof step 20 from proof perm-put-del1 (previous step)

n < # y, a0 ∈ y[n, a] -1l a ∨ a0 ∈ y ⊦ #oc(a0, y[n, a] -1l a) = #oc(a0, y), a0 = y[n], y = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ a ≠ b → #oc(a, x -1l b) = #oc(a, x)
Proof step 22:
a0 = a, n < # y, a0 ∈ y[n, a] -1l a ∨ a0 ∈ y ⊦ #oc(a0, y[n, a] -1l a) = #oc(a0, y), a0 = y[n], y = []

Rule argument

spec: <toplevel> name: del1-01 seq: ⊦ a ≠ b → #oc(a, x -1l b) = #oc(a, x) subst: [b, x, a] → [a, y[n, a], a0] flags: <all paths>

Additional information

Used simplifier rules: ocs-put-01: ⊦ x[m] ≠ a ∧ a ≠ b ∧ m < # x → #oc(a, x[m, b]) = #oc(a, x); Used terms: a, y[n, a], a0