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Proof step 6 from proof prefix-split-stronger (previous step)

x0 ⊑ y0 + z, ∀ y, z. x0 ⊑ y + z → x0 ⊑ y ∨ (∃ x1. x0 = y + x1 ∧ x1 ⊑ z), ∀ 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) ⊦ x0 ⊑ y0, ∃ x. x0 = y0 + x ∧ x ⊑ z

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 2 terms: y0, z

Additional information

Used simplifier rules: postifx-app-03: ⊦ x + y ⊑ x + z ↔ y ⊑ z;%prefix-app-01: ⊦ x + y ⊑ x ↔ y = [];%a: ⊦ (x + y) + z = x + y + z; from specification list%app-01: ⊦ x + y = x + z ↔ y = z; from specification list Used terms: y0, z