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Proof step 8 from proof range-eq-bounds (previous step)

ar0[n0] = ar1[n1], range=(ar0, n0 + 1, ar1, n1 + 1, m0), # ar1 ≤ m0 + n1, ∀ ar0, n0, ar1, n1. range=(ar0, n0, ar1, n1, m0) → n0 + m0 ≤ # ar0 ∧ n1 + m0 ≤ # ar1 ⊦ n0 + m0 < # ar0 ∧ n1 + m0 < # ar1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
ar0[n0] = ar1[n1], range=(ar0, n0 + 1, ar1, n1 + 1, m0), # ar1 ≤ m0 + n1, ∀ ar0, n0, ar1, n1. range=(ar0, n0, ar1, n1, m0) → n0 + m0 ≤ # ar0 ∧ n1 + m0 ≤ # ar1 ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ n → (n < m ↔ false); (s)%c: ⊦ m + n = n + m; from specification nat-basic