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

a < a0, b < a0, ordered≤(a0 ' + y + z), b ∈ y, ∀ 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: <toplevel> name: orderedle-ls seq: ⊦ b < a ∧ b ∈ x → ¬ ordered≤(a ' + x) subst: [b, x, a] → [b, y + z, a0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ a ∈ x → a ∈ x + y; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: b, y + z, a0