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Proof step 11 from proof inv-add-log-leb (previous step)

# lpt = # avol, avol[m3] = mapped(buf), m3 < # avol, awbuf-inv(avol, bleb), synced(avol) ⊦ awbuf-inv(avol, buffered(m3))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: awbuf-inv name: awbuf-inv-def seq: ⊦ 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?)) subst: [bleb, avol] → [buffered(m3), avol] flags: <all paths>

Additional information

Used simplifier rules: ⊦ buffered(m) = buffered(m0) ↔ m = m0; (s)% ⊦ nobuffer ≠ buffered(m); (s)% ⊦ buffered(m).leb = m; (s)% ⊦ mapped(buf).mapped?; (s)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ mapped(buf).data = buf; (s)%⊦ n < # avol ∧ synced(avol) ∧ avol[n] = mapped(buf) → is-aligned(# buf, EB_PAGE_SIZE); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%⊦ awbuf-inv(avol, bleb) ∧ n < # avol ∧ avol[n] = mapped(buf) → ¬ LEB_SIZE < # buf; (s) Used terms: buffered(m3), avol