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Proof step 4 from proof len-01 (previous step)

#(a0 + x0) < pos(a, a0 + x0), ∀ a. ¬ # x0 < pos(a, x0) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
1 + # x0 < pos(a, a0 ' + x0), ∀ a. ¬ # x0 < pos(a, x0) ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ # a ' = 0 +1; (s)% ⊦ #(x + y) = # x + # y; (s)% ⊦ a + x = a ' + x; (s)