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Proof step 1 from proof ins-y-01 (conclusion)

⊦ a < b → ins≤(a, b ' + x) = a + b + x

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ ¬ b < a → ins≤(a, b ' + x) = a + b + x

Rule argument

spec: olist inst: name: ins-y seq: ⊦ ¬ b < a → ins≤(a, b ' + x) = a + b + x subst: [x, b, a] → [x, b, a] flags: rewrite, current

Additional information

Used simplifier rules: ins-n: ⊦ b < a → ins≤(a, b ' + x) = b + ins≤(a, x);%c: ⊦ a + x = a ' + x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%transitivity: ⊦ a < b ∧ b < c → a < c; (forward) from specification oelem%irreflexivity: ⊦ ¬ a < a; from specification oelem Used terms: x, b, a