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Proof step 9 from proof ocs-del-length (previous step)

∀ a, b. #oc(a, x0 -l b) = #oc(a, x0) ∨ a = b ⊦ #oc(a, (a0 ' + x0) -l b) = #oc(a, x0), a = a0, a = b

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ a ≠ b → (b ' + x) -l a = b ' + (x -l a)
Proof step 11:
b = a0, ∀ a, b. #oc(a, x0 -l b) = #oc(a, x0) ∨ a = b ⊦ #oc(a, (a0 ' + x0) -l b) = #oc(a, x0), a = b, a = a0
Proof step 13:
∀ a, b. #oc(a, x0 -l b) = #oc(a, x0) ∨ a = b ⊦ #oc(a, a0 ' + (x0 -l b)) = #oc(a, x0), a = b, a = a0, b = a0

Rule argument

spec: list-del name: del-n seq: ⊦ a ≠ b → (b ' + x) -l a = b ' + (x -l a) subst: [a, x, b] → [b, x0, a0] flags: <all paths>

Additional information

Used terms: b, x0, a0