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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
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

Rule argument

Additional information

Used simplifier rules: sls: ⊦ a ≠ b → (¬ a < b ↔ b < a); 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