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Proof step 9 from proof del1 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: c-08: ⊦ (a ' + x).first = a; from specification list%e-01: ⊦ a ' + x ≠ []; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%c-07: ⊦ (a ' + x).rest = x; from specification list