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Proof step 4 from proof rangeeq-till-leb5-fwd (previous step)

m < 5, 0 + 5 + n ≤ # avol1, 0 + 5 + n ≤ # avol0, ∀ n2. n2 < 5 + n → avol1[0 + n2] = avol0[0 + n2] ⊦ avol1[m] = avol0[m]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
m < 5, 5 + n ≤ # avol0, 5 + n ≤ # avol1, ∀ n0. n0 < 5 + n → avol1[n0] = avol0[n0] ⊦ avol1[m] = avol0[m]

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ n + 0 = n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic