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Proof step 64 from proof inv-allocate-ind (previous step)

# lpt2 = # avol0, # lpt0 = # avol0, lpt2[n0] = mklp(0, m3, LP_FREE, m2), keyset(gch) = gc-heap(lpt2, log0), n0 < # avol0, awbuf-inv(avol0[n0, mapped(mkbuf(0))], buffered(n0)), awbuf-inv(avol0[n0, mapped(mkbuf(0))], bleb), awbuf-inv(avol0, bleb), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, bleb, lpt2, avol0), bufs-log-only(bleb, log0, lpt2), freelist-cons(lpt2, n0 ' + nx0), log-group-block(log0, lpt2), lpt-free-unref(lpt0), lpt-free-unref(lpt2), lpt-leb-size(lpt0), lpt-leb-size(lpt2), lpt-ram-flash(lpt2, lpt0, log0), synced(avol0), bleb ≠ nobuffer → avol0[n0, mapped(mkbuf(0))][bleb.leb].mapped? ∧ bleb.leb < # avol0 ∧ bleb.isbuf?, bleb = nobuffer ∨ is-aligned(# avol0[n0, mapped(mkbuf(0))][bleb.leb].data, EB_PAGE_SIZE) ⊦ buffered(n0) = bleb, bufs-log-only(buffered(n0), log0, lpt2[n0, mklp(0, 0, LP_INDEX_NODES, m2)])

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: persistence-base name: bufs-log-only seq: ⊦ bufs-log-only(bleb, nx, lpt) ↔ bleb = nobuffer ∨ bleb.leb < # lpt ∧ ( nx ≠ [] ∧ bleb.leb = nx.last ∧ lpt[bleb.leb].flags = LP_GROUP_NODES ∨ lpt[bleb.leb].flags = LP_INDEX_NODES) subst: [lpt, nx, bleb] → [lpt2[n0, mklp(0, 0, LP_INDEX_NODES, m2)], log0, buffered(n0)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ nobuffer ≠ buffered(m); (s)% ⊦ buffered(m).leb = m; (s)% ⊦ # lpt[n, lp] = # lpt; (s)% ⊦ m < # lpt → lpt[m, lp][m] = lp; (s)% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)% ⊦ LP_GROUP_NODES ≠ LP_INDEX_NODES; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%freelist-cons-first-free: ⊦ freelist-cons(lpt, n ' + freelist) → n < # lpt ∧ lpt[n].flags = LP_FREE; (forward) from specification persistence-base%a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]%inv-buf-in-vol: ⊦ awbuf-inv(avol, buffered(n)) → n < # avol; (forward) from specification awbuf-inv%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ # avol[n, aleb] = # avol; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)%m ≠ n ⊦ avol[m, aleb][n] = avol[n]; (s)% ⊦ bleb.isbuf? ↔ (∃ n. bleb = buffered(n)); (as)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ ¬ n < n; (s) Used terms: lpt2[n0, mklp(0, 0, LP_INDEX_NODES, m2)], log0, buffered(n0)