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

awbuf-inv(avol, buffered(n)) ⊦ awbuf-inv(avol[n, mapped(buf)], buffered(n)) ↔ # avol[n].data ≤ LEB_SIZE → # buf ≤ LEB_SIZE

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
avol[n] = mapped(buf0), n < # avol, ∀ n0. n0 < # avol ∧ avol[n0].mapped? → # avol[n0].data ≤ LEB_SIZE ∧ (n0 ≠ n → is-aligned(# avol[n0].data, EB_PAGE_SIZE)) ⊦ (∀ n0. n0 < # avol ∧ avol[n, mapped(buf)][n0].mapped? → # avol[n, mapped(buf)][n0].data ≤ LEB_SIZE ∧ (n0 ≠ n → is-aligned(# avol[n0].data, EB_PAGE_SIZE))) ↔ # buf0 ≤ LEB_SIZE → # buf ≤ LEB_SIZE

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?));% ⊦ mapped(buf).data = buf; (s)% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)% ⊦ mapped(buf).mapped?; (s)% ⊦ m < # avol → avol[m, aleb][m] = aleb; (s)% ⊦ buffered(m).leb = m; (s)% ⊦ nobuffer ≠ buffered(m); (s)% ⊦ m ≠ n → avol[n, aleb][m] = avol[m]; (s)% ⊦ buffered(m) = buffered(m0) ↔ m = m0; (s)% ⊦ # avol[n, aleb] = # avol; (s)