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Proof step 11 from proof del1 (previous step)

x0 -1l a = a2 + y, ordered<(a0 ' + x0), ∀ a1. ordered<(x0 -1l a1) ⊦ a = a0, x0 -1l a = [], a0 < a2 ∧ ordered<(x0 -1l a)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
x0 -1l a = a2 ' + y, a2 ∈ x0 -1l a, ordered<(a0 ' + x0), a2 ∈ x0, ∀ a1. ordered<(x0 -1l a1) ⊦ x0 -1l a = [], a = a0, a0 < a2 ∧ ordered<(x0 -1l a)

Rule argument

Additional information

Used simplifier rules: in-01-01: ⊦ a ∈ x -1l b → a ∈ x; (forward) from specification list-del%a: ⊦ (x + y) + z = x + y + z; from specification list%in-14: ⊦ a ' + x = y → a ∈ y; (forward) from specification list%c: ⊦ a + x = a ' + x; from specification list