| # lpt0 = # avol0, # lpt2 = # avol0, lpt2[n0] = mklp(0, m3, LP_FREE, m2), err = err0, freelist = (n0 ' + nx0).tail, keyset(gch) = gc-heap(lpt2, log0), lpt1 = lpt2[n0, lpt2[n0, mklp(lpt2[n0].ref-size, 0, lpt2[n0].flags, lpt2[n0].gcheapidx)][n0].ref-size:= 0], n0 < # avol0, n0 < # lpt2[n0, mklp(lpt2[n0].ref-size, 0, lpt2[n0].flags, lpt2[n0].gcheapidx)], n0 < # lpt2, awbuf-inv(avol0, bleb), awbuf-inv(avol0[n0, mapped(mkbuf(0))], 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(lpt2), lpt-free-unref(lpt0), lpt-leb-size(lpt2), lpt-leb-size(lpt0), lpt-ram-flash(lpt2, lpt0, log0), synced(avol0), bleb ≠ nobuffer → avol0[n0, mapped(mkbuf(0))][bleb.leb].mapped? ∧ bleb.leb < # avol0 ∧ bleb.isbuf?, ⌊err0⌋ ∨ err0 = ESUCCESS, bleb = nobuffer ∨ is-aligned(# avol0[n0, mapped(mkbuf(0))][bleb.leb].data, EB_PAGE_SIZE) ⊦ ⟪freelist := n0 ' + freelist⟫ ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log0) ∧ bufs-log-only(bleb, log0, lpt1) ∧ # lpt1 = # avol0 ∧ log-group-block(log0, lpt1) ∧ buf-ro-rw-mode(false, bleb, lpt1, avol0[n0, mapped(mkbuf(0))]) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log0)), n0 ' + nx0 = [], buffered(n0) = bleb, err = ESUCCESS |
Used simplifier rules: ⊦ n ' + nx ≠ []; (s)%a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]% ⊦ # lpt[n, lp] = # lpt; (s)% ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s)% ⊦ m < # lpt → lpt[m, lp][m] = lp; (s)% ⊦ mklp(m, m0, lpf, m1).ref-size:= m2 = mklp(m2, m0, lpf, m1); (s)%⊦ lpt-free-unref(lpt) → ( lpt-free-unref(lpt[n, lp]) ↔ n < # lpt ∧ lp.flags = LP_FREE → lp.ref-size = 0); (s)% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)% ⊦ mklp(n2, n3, lpf, m).ref-size = n2; (s)% ⊦ (n ' + nx).tail = nx; (s)% ⊦ LP_FREE ≠ LP_GROUP_NODES; (s)%lpf0 ≠ LP_GROUP_NODES, n < # lpt ⊦ lpt[n] = mklp(m0, m1, lpf0, m2) ∧ keyset(gch) = gc-heap(lpt, nx) → ( bin-heap-inv(gch, lpt[n, mklp(n0, n1, lpf1, n2)]) ↔ bin-heap-inv(gch, lpt)); (s)%lpf0 ≠ LP_GROUP_NODES, lpf1 ≠ LP_GROUP_NODES, n < # lpt ⊦ lpt[n] = mklp(m0, m1, lpf0, m2) → gc-heap(lpt[n, mklp(n0, n1, lpf1, n2)], nx) = gc-heap(lpt, nx); (s)% ⊦ mklp(n2, n3, lpf, m).gcheapidx = m; (s)%lpt[n].flags = lp.flags ⊦ bufs-log-only(bleb, nx, lpt) → bufs-log-only(bleb, nx, lpt[n, lp]); (s)%n < # lpt, lpf ≠ LP_GROUP_NODES ⊦ lpt[n] = mklp(n0, n1, lpf, n2) ∧ log-group-block(nx, lpt) → log-group-block(nx, lpt[n, lp]); (s)%⊦ bleb ≠ buffered(n) → ( buf-ro-rw-mode(boolvar, bleb, lpt[n, lp], avol) ↔ buf-ro-rw-mode(boolvar, bleb, lpt, avol)); (s)%⊦ bleb ≠ buffered(n) → ( buf-ro-rw-mode(boolvar, bleb, lpt, avol[n, aleb]) ↔ buf-ro-rw-mode(boolvar, bleb, lpt, avol)); (s)%⊦ lpt-leb-size(lpt) → (lpt-leb-size(lpt[n, lp]) ↔ # lpt ≤ n ∨ lp.size ≤ LEB_SIZE); (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ mklp(n2, n3, lpf, m).size = n3; (s)% ⊦ 0 ≤ m; (s)%n < # lpt, lpf ≠ LP_GROUP_NODES ⊦ lpt-ram-flash(lpt, lpt0, nx) → lpt-ram-flash(lpt[n, mklp(n0, n1, lpf, n2)], lpt0, nx); (ss)%⊦ freelist-cons(lpt, freelist) ∧ lpt[n] = mklp(m0, m1, lpf, m2) → freelist-cons(lpt[n, mklp(n0, n1, lpf, n2)], freelist); (s)