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Proof step 7 from proof lebs-idexpt-below (previous step)

# avol1 = # avol0, lebs(avol1, m0, m) = lebs(avol0, m0, m), n < m0, m0 + m < # avol0, id○(avol1, avol0, n) ⊦ (avol1[m0 + m].mapped? ⊃ avol1[m0 + m].data + mkempbuf(LEB_SIZE - # avol1[m0 + m].data);mkempbuf(LEB_SIZE)) = (avol0[m0 + m].mapped? ⊃ avol0[m0 + m].data + mkempbuf(LEB_SIZE - # avol0[m0 + m].data);mkempbuf(LEB_SIZE))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ id○(avol, avol0, n) ↔ # avol = # avol0 ∧ (∀ m. m < # avol ∧ m ≠ n → avol[m] = avol0[m])
Proof step 9:
# avol1 = # avol0, lebs(avol1, m0, m) = lebs(avol0, m0, m), m0 + m < # avol0, n < m0, ∀ m. m < # avol1 ∧ m ≠ n → avol1[m] = avol0[m] ⊦ (avol1[m0 + m].mapped? ⊃ avol1[m0 + m].data + mkempbuf(LEB_SIZE - # avol1[m0 + m].data);mkempbuf(LEB_SIZE)) = (avol0[m0 + m].mapped? ⊃ avol0[m0 + m].data + mkempbuf(LEB_SIZE - # avol0[m0 + m].data);mkempbuf(LEB_SIZE))

Rule argument

spec: array-copy, inst: avolume name: Idexcept seq: ⊦ id○(avol, avol0, n) ↔ # avol = # avol0 ∧ (∀ m. m < # avol ∧ m ≠ n → avol[m] = avol0[m]) subst: [n, avol0, avol] → [n, avol0, avol1] flags: <all paths>

Additional information

Used terms: n, avol0, avol1