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Proof step 5 from proof del-length (previous step)

a = a0, # x0 + 1 < #((a0 ' + x0) -l a), ∀ a. # x0 < #(x0 -l a) → x0 -l a = [] ⊦ (a0 ' + x0) -l a = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
# x0 + 1 < #(x0 -l a0), ∀ a. # x0 < #(x0 -l a) → x0 -l a = [] ⊦ x0 -l a0 = []

Rule argument

Additional information

Used simplifier rules: del-y: ⊦ (a ' + x) -l a = x -l a;%l: ⊦ # x = 0 ↔ x = []; from specification list-data%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%a: ⊦ (x + y) + z = x + y + z; from specification list