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Proof step 13 from proof ordered-ex-divide-lsle (previous step)

ordered≤(a0 ' + y + z), b < a, ∀ b. b ∈ z → b = a ∨ a < b, ∀ b. b ∈ y → b < a, b ∈ y ∨ b ∈ z ⊦ b = a, a0 < a

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ b < a ∧ b ∈ x → ¬ ordered≤(a ' + x)

Rule argument

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

Additional information

Used simplifier rules: in-append: ⊦ a ∈ x + y ↔ ¬ ¬(a ∈ x ∨ a ∈ y); from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%nll: ⊦ ¬ b < a ∧ b < c → a < c; (forward) from specification oelem%nnn: ⊦ ¬ c < b ∧ ¬ a < c → ¬ a < b; (forward) from specification oelem Used terms: b, y + z, a0