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Proof step 5 from proof rangeeq-write-right-concrete-below (previous step)

n0 < n ⊦ (n + m) + m1 ≤ # avol ∧ (n + m) + m1 ≤ # avol0 ∧ (∀ n1. n1 < m1 → avol[(n + m) + n1] = avol0[(n + m) + n1]) ↔ range=(avol, n + m, avol0, n + m, m1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ range=(avol, n0, avol0, n1, m) ↔ n0 + m ≤ # avol ∧ n1 + m ≤ # avol0 ∧ (∀ n. n < m → avol[n0 + n] = avol0[n1 + n])

Rule argument

spec: array-splice, inst: avolume name: range-eq-ext seq: ⊦ range=(avol, n0, avol0, n1, m) ↔ n0 + m ≤ # avol ∧ n1 + m ≤ # avol0 ∧ (∀ n. n < m → avol[n0 + n] = avol0[n1 + n]) subst: [m, n1, avol0, n0, avol] → [m1, n + m, avol0, n + m, avol] flags: <all paths>

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: m1, n + m, avol0, n + m, avol