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Proof step 2 from proof sum-equal (previous step)

# ints = # ints0, ∀ n. n < # ints0 → ints[n] = ints0[n] ⊦ Σ ints = Σ ints0

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ ints0. # ints1 = # ints0 ∧ (∀ n. n < # ints0 → ints1[n] = ints0[n]) → Σ ints1 = Σ ints0, #(i + ints1) = # ints0, ∀ n. n < # ints0 → (i + ints1)[n] = ints0[n] ⊦ Σ(i + ints1) = Σ ints0

Rule argument

indvar: ints

Additional information

Used simplifier rules: intlist freely generated by [], +;;%size-01: ⊦ # [] = 0; from specification list-data[intlista]%l: ⊦ # ints = 0 ↔ ints = []; from specification list-data[intlista]