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Proof step 4 from proof prefix-split-stronger (previous step)

a ' + x0 ⊑ y + z, ∀ y, z. x0 ⊑ y + z → x0 ⊑ y ∨ (∃ x1. x0 = y + x1 ∧ x1 ⊑ z) ⊦ a ' + x0 ⊑ y, ∃ x. a ' + x0 = y + x ∧ x ⊑ z

User applied rule structural induction

And obtained the following new goals

Proof step 5:
∀ a, x0, z. a ' + x0 ⊑ y0 + z ∧ (∀ y, z. x0 ⊑ y + z → x0 ⊑ y ∨ (∃ x1. x0 = y + x1 ∧ x1 ⊑ z)) → a ' + x0 ⊑ y0 ∨ (∃ x. a ' + x0 = y0 + x ∧ x ⊑ z), a ' + x0 ⊑ (a0 + y0) + z, ∀ y, z. x0 ⊑ y + z → x0 ⊑ y ∨ (∃ x1. x0 = y + x1 ∧ x1 ⊑ z) ⊦ a ' + x0 ⊑ a0 + y0, ∃ x. a ' + x0 = (a0 + y0) + x ∧ x ⊑ z

Rule argument

indvar: y

Additional information

Used simplifier rules: prefix-empty: ⊦ x ⊑ [] ↔ x = [];%list freely generated by [], +;;%Nil: ⊦ [] + x = x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%e-01: ⊦ a ' + x ≠ []; from specification list