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Proof step 27 from proof recovery (previous step)

ebm-cons(avols1), ebm-cons(avols0), ebm-vol-inv(abs(avols1[default-volid])), default-volid ∈ avols1, avols1 ⊆ avols0 ⊦ abs(avols1[default-volid]) ⊆ abs(avols0[default-volid])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
⊦ avol0 ⊆ avol1 ↔ # avol0 = # avol1 ∧ (∀ m. m < # avol0 → (avol0[m].mapped? → avol1[m] = avol0[m]) ∧ (avol0[m] = unmapped ∧ avol1[m].mapped? → # avol1[m].data ≤ LEB_SIZE ∧ is-aligned(# avol1[m].data, EB_PAGE_SIZE)))
Proof step 29:
ebm-cons(avols0), ebm-cons(avols1), ebm-vol-inv(abs(avols1[default-volid])), default-volid ∈ avols1, avols1 ⊆ avols0 ⊦ # abs(avols1[default-volid]) = # abs(avols0[default-volid]) ∧ (∀ m. m < # abs(avols1[default-volid]) → (abs(avols1[default-volid])[m].mapped? → abs(avols0[default-volid])[m] = abs(avols1[default-volid])[m]) ∧ ( abs(avols1[default-volid])[m] = unmapped ∧ abs(avols0[default-volid])[m].mapped? → # abs(avols0[default-volid])[m].data ≤ LEB_SIZE ∧ is-aligned(# abs(avols0[default-volid])[m].data, EB_PAGE_SIZE)))

Rule argument

spec: ebm-vol-inv name: ebm-vol-le seq: ⊦ avol0 ⊆ avol1 ↔ # avol0 = # avol1 ∧ (∀ m. m < # avol0 → (avol0[m].mapped? → avol1[m] = avol0[m]) ∧ ( avol0[m] = unmapped ∧ avol1[m].mapped? → # avol1[m].data ≤ LEB_SIZE ∧ is-aligned(# avol1[m].data, EB_PAGE_SIZE))) subst: [avol1, avol0] → [abs(avols0[default-volid]), abs(avols1[default-volid])] flags: <all paths>

Additional information

Used terms: abs(avols0[default-volid]), abs(avols1[default-volid])