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Proof step 2 from proof len (previous step)

∀ a. # ins≤(a, x0) = # x0 + 1 ⊦ # ins≤(a, a0 + x0) = #(a0 + x0) + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
∀ a. # ins≤(a, x0) = # x0 + 1 ⊦ # ins≤(a, a0 ' + x0) = (1 + # x0) + 1

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ # a ' = 0 +1; (s)% ⊦ #(x + y) = # x + # y; (s)% ⊦ a + x = a ' + x; (s)