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Proof step 2 from proof put-in-02 (previous step)

m < # x ⊦ a ∈ x[m, a]

User applied rule structural induction

And obtained the following new goals

Proof step 3:
m < #(a0 + x0), ∀ m, a. m < # x0 → a ∈ x0[m, a] ⊦ a ∈ (a0 + x0)[m, a]

Rule argument

indvar: x

Additional information

Used simplifier rules: list freely generated by [], +;;% ⊦ # [] = 0; (s)% ⊦ ¬ n < 0; (s)