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Proof step 7 from proof range-eq-bounds (previous step)

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

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 8:
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
Proof step 10:
ar0[n0] = ar1[n1], range=(ar0, n0 + 1, ar1, n1 + 1, m0), ∀ ar0, n0, ar1, n1. range=(ar0, n0, ar1, n1, m0) → n0 + m0 ≤ # ar0 ∧ n1 + m0 ≤ # ar1 ⊦ # ar1 ≤ m0 + n1, n0 + m0 < # ar0 ∧ n1 + m0 < # ar1

Rule argument

fma: # ar1 ≤ m0 + n1

Additional information

Used formulas: # ar1 ≤ m0 + n1