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Proof step 15 from proof ordered-ex-divide-lels (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ 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-11: ⊦ a ∈ x → a ∈ x + y; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: b, y + z, a0