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Proof step 23 from proof orderedle-all (previous step)

m1 < # y, y[m1] < a, ordered≤(a0 ' + y), ∀ m, n. m ≤ n ∧ n < 1 + # y → ¬ (a0 ' + y)[n] < (a0 ' + y)[m] ⊦ y = [], a0 < a

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ b < a ∧ b ∈ x → ¬ ordered≤(a ' + x)

Rule argument

spec: olist inst: name: orderedle-ls seq: ⊦ b < a ∧ b ∈ x → ¬ ordered≤(a ' + x) subst: [b, a, x] → [y[m1], a0, y] flags: rewrite, current

Additional information

Used simplifier rules: get-in: ⊦ m < # x → (¬ x[m] ∈ x ↔ false); from specification list-del%nll: ⊦ ¬ b < a ∧ b < c → a < c; (forward) from specification oelem%nnn: ⊦ ¬ c < b ∧ ¬ a < c → ¬ a < b; (forward) from specification oelem Used terms: y[m1], a0, y