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Proof step 11 from proof delapp (previous step)

#oc(a1, y0) + #oc(a1, y) < #oc(a1, y -1l a), ∀ a0. #oc(a0, y -1l a) ≤ (#oc(a0, a1 ') + #oc(a0, y0)) + #oc(a0, y), ∀ a0. (#oc(a0, a1 ') + #oc(a0, y0)) + #oc(a0, y) ≤ #oc(a0, y -1l a) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ a ≠ b → #oc(a, x -1l b) = #oc(a, x)
Proof step 13:
¬ a1 ≠ a, #oc(a1, y0) + #oc(a1, y) < #oc(a1, y -1l a), ∀ a0. #oc(a0, y -1l a) ≤ (#oc(a0, a1 ') + #oc(a0, y0)) + #oc(a0, y), ∀ a0. (#oc(a0, a1 ') + #oc(a0, y0)) + #oc(a0, y) ≤ #oc(a0, y -1l a) ⊦

Rule argument

spec: list-perm inst: name: del1-01 seq: ⊦ a ≠ b → #oc(a, x -1l b) = #oc(a, x) subst: [b, x, a] → [a, y, a1] flags: rewrite, current

Additional information

Used simplifier rules: l-02: ⊦ ¬ m + n < m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used terms: a, y, a1