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Proof step 19 from proof lastoc (previous step)

disj(y0, x1), b ∈ x1, a ∈ x1, disj(x1, y0), ∀ a, x0. a ∈ x1 ∧ a ∈ x0 → (∃ b, y, y0. b ∈ x1 ∧ x0 = y + b ' + y0 ∧ disj(x1, y0)), a ∈ y ∨ a = b ⊦ a ∈ y0, b ∈ y0, ∃ b0, y1, y2. (b0 = a0 ∨ b0 ∈ x1) ∧ y + b ' + y0 = y1 + b0 ' + y2 ∧ disj(a0 ' + x1, y2)

User applied rule exists right

And obtained the following new goals

Proof step 20:
disj(y0, x1), b ∈ x1, a ∈ x1, disj(x1, y0), ∀ a, x0. a ∈ x1 ∧ a ∈ x0 → (∃ b, y, y0. b ∈ x1 ∧ x0 = y + b ' + y0 ∧ disj(x1, y0)), a ∈ y ∨ a = b ⊦ a ∈ y0, b ∈ y0, (b = a0 ∨ b ∈ x1) ∧ y + b ' + y0 = y + b ' + y0 ∧ disj(a0 ' + x1, y0), ∃ b0, y1, y2. (b0 = a0 ∨ b0 ∈ x1) ∧ y + b ' + y0 = y1 + b0 ' + y2 ∧ disj(a0 ' + x1, y2)

Rule argument

pos: right 3 terms: b, y, y0 abort: F discard: F computed: T

Additional information

Used terms: b, y, y0