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Proof step 4 from proof append-size-less (previous step)

(a ' + x3) + x0 = x1 + x2, # x3 + 1 < # x1, ∀ x0, x1, x2. x3 + x0 = x1 + x2 ∧ # x3 < # x1 → x1 = [] ∨ (∃ y. x1 = x3 + y ∧ x0 = y + x2), a ∈ x1 ∨ a ∈ x2 ⊦ x1 = [], ∃ y. x1 = (a ' + x3) + y ∧ x0 = y + x2

User applied rule constructor cut

And obtained the following new goals

Proof step 5:
x1 = a0 + x, (a ' + x3) + x0 = x1 + x2, # x3 + 1 < # x1, ∀ x0, x1, x2. x3 + x0 = x1 + x2 ∧ # x3 < # x1 → x1 = [] ∨ (∃ y. x1 = x3 + y ∧ x0 = y + x2), a ∈ x1 ∨ a ∈ x2 ⊦ x1 = [], ∃ y. x1 = (a ' + x3) + y ∧ x0 = y + x2

Rule argument

var: x1

Additional information

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