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Proof step 12 from proof ordered-ex-divide-lels (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
ordered≤(a0 ' + y + z), a < a0, b < a0, ∀ b. b ∈ z → a < b, ∀ b. b ∈ y → b < a ∨ b = a, b ∈ y ∨ b ∈ z ⊦ a0 = a, a < b

Rule argument

Additional information

Used simplifier rules: nll: ⊦ ¬ b < a ∧ b < c → a < c; (forward) from specification oelem%in-append: ⊦ a ∈ x + y ↔ ¬ ¬(a ∈ x ∨ a ∈ y); from specification list%in-rec: ⊦ a ∈ b ' + x ↔ ¬ ¬(a = b ∨ a ∈ x); from specification list%in-empty: ⊦ ¬ a ∈ []; from specification list%app-08: ⊦ a ' + x = a ' + y ↔ x = y; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%Nil: ⊦ [] + x = x; from specification list