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Proof step 2 from proof inv-write-unbuf (previous step)

n < # avol, awbuf-inv(avol, bleb) ⊦ awbuf-inv(avol[n, mapped(buf)], bleb) ↔ (avol[n].mapped? → # avol[n].data ≤ LEB_SIZE ∧ is-aligned(# avol[n].data, EB_PAGE_SIZE)) → # buf ≤ LEB_SIZE ∧ is-aligned(# buf, EB_PAGE_SIZE), bleb = buffered(n)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
n < # avol, bleb ≠ nobuffer → bleb.leb < # avol ∧ avol[bleb.leb].mapped?, ∀ n. n < # avol ∧ avol[n].mapped? → # avol[n].data ≤ LEB_SIZE ∧ (buffered(n) ≠ bleb → is-aligned(# avol[n].data, EB_PAGE_SIZE)) ⊦ (∀ n0. n0 < # avol ∧ avol[n, mapped(buf)][n0].mapped? → # avol[n, mapped(buf)][n0].data ≤ LEB_SIZE ∧ (buffered(n0) ≠ bleb → is-aligned(# avol[n, mapped(buf)][n0].data, EB_PAGE_SIZE))) ∧ (bleb ≠ nobuffer → bleb.leb < # avol ∧ avol[n, mapped(buf)][bleb.leb].mapped?) ↔ (avol[n].mapped? → # avol[n].data ≤ LEB_SIZE ∧ is-aligned(# avol[n].data, EB_PAGE_SIZE)) → # buf ≤ LEB_SIZE ∧ is-aligned(# buf, EB_PAGE_SIZE), bleb = buffered(n)

Rule argument

Additional information

Used simplifier rules: awbuf-inv-def: ⊦ awbuf-inv(avol, bleb) ↔ ¬ ¬ ( (∀ n. n < # avol ∧ avol[n].mapped? → # avol[n].data ≤ LEB_SIZE ∧ ( buffered(n) ≠ bleb → is-aligned(# avol[n].data, EB_PAGE_SIZE))) ∧ (bleb ≠ nobuffer → bleb.leb < # avol ∧ avol[bleb.leb].mapped?));% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ # avol[n, aleb] = # avol; (s)