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Proof step 19 from proof lebs-range-eq (previous step)

lebs(avol0, n0, n) = lebs(avol1, n0, n), n0 + n < # avol1, n0 + n < m + m2, n0 + n < # avol0, range=(avol0, m, avol1, m, m2), m ≤ n0 ⊦ (avol0[n0 + n].mapped? ⊃ avol0[n0 + n].data + mkempbuf(LEB_SIZE - # avol0[n0 + n].data);mkempbuf(LEB_SIZE)) = (avol1[n0 + n].mapped? ⊃ avol1[n0 + n].data + mkempbuf(LEB_SIZE - # avol1[n0 + n].data);mkempbuf(LEB_SIZE))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ range=(avol, n0, avol0, n1, m) ↔ n0 + m ≤ # avol ∧ n1 + m ≤ # avol0 ∧ (∀ n. n < m → avol[n0 + n] = avol0[n1 + n])
Proof step 21:
lebs(avol0, n0, n) = lebs(avol1, n0, n), n0 + n < # avol0, n0 + n < m + m2, n0 + n < # avol1, m ≤ n0, m + m2 ≤ # avol0, m + m2 ≤ # avol1, ∀ n. n < m2 → avol0[m + n] = avol1[m + n] ⊦ (avol0[n0 + n].mapped? ⊃ avol0[n0 + n].data + mkempbuf(LEB_SIZE - # avol0[n0 + n].data);mkempbuf(LEB_SIZE)) = (avol1[n0 + n].mapped? ⊃ avol1[n0 + n].data + mkempbuf(LEB_SIZE - # avol1[n0 + n].data);mkempbuf(LEB_SIZE))

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] → [m2, m, avol1, m, avol0] flags: <all paths>

Additional information

Used terms: m2, m, avol1, m, avol0