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Proof step 13 from proof ordered-ex-divide-lels (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 14:
b < a0, a < a0, ordered≤(a0 ' + y + z), b ∈ y, ∀ b. b ∈ y → b < a ∨ b = a, ∀ b. b ∈ z → a < b ⊦ a0 = a, a < b
Proof step 17:
b < a0, a < a0, ordered≤(a0 ' + y + z), b ∈ z, ∀ b. b ∈ y → b < a ∨ b = a, ∀ b. b ∈ z → a < b ⊦ a0 = a, a < b

Rule argument

pos: left 6

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