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Proof step 1 from proof ordered-ex-divide-lels (conclusion)

ordered≤(x) ⊦ ∃ y, z. x = y + z ∧ (∀ b. b ∈ y → b < a ∨ b = a) ∧ (∀ b. b ∈ z → a < b)

User applied rule structural induction

And obtained the following new goals

Proof step 2:
ordered≤([]) ⊦ ∃ y, z. [] = y + z ∧ (∀ b. b ∈ y → b < a ∨ b = a) ∧ (∀ b. b ∈ z → a < b)
Proof step 4:
∀ a. ordered≤(x0) → (∃ y, z. x0 = y + z ∧ (∀ b. b ∈ y → b < a ∨ b = a) ∧ (∀ b. b ∈ z → a < b)), ordered≤(a0 + x0) ⊦ ∃ y, z. a0 + x0 = y + z ∧ (∀ b. b ∈ y → b < a ∨ b = a) ∧ (∀ b. b ∈ z → a < b)

Rule argument

indvar: x

Additional information

Used simplifier rules: list freely generated by [], +;;