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Proof step 7 from proof ordered-ex-divide-lsle (previous step)

ordered≤(a0 ' + y + z), ∀ b. b ∈ z → b = a ∨ a < b, ∀ b. b ∈ y → b < a ⊦ ∃ y0, z0. a0 ' + y + z = y0 + z0 ∧ (∀ b. b ∈ y0 → b < a) ∧ (∀ b. b ∈ z0 → b = a ∨ a < b)

User applied rule exists right

And obtained the following new goals

Proof step 8:
ordered≤(a0 ' + y + z), ∀ b. b ∈ z → b = a ∨ a < b, ∀ b. b ∈ y → b < a ⊦ a0 ' + y + z = (a0 ' + y) + z ∧ (∀ b. b ∈ a0 ' + y → b < a) ∧ (∀ b. b ∈ z → b = a ∨ a < b), ∃ y0, z0. a0 ' + y + z = y0 + z0 ∧ (∀ b. b ∈ y0 → b < a) ∧ (∀ b. b ∈ z0 → b = a ∨ a < b)

Rule argument

pos: right 1 terms: a0 ' + y, z abort: F discard: F computed: T

Additional information

Used terms: a0 ' + y, z