[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 38 from proof inv-sync (previous step)

# lpt1 = # avol, # lpt0 = # avol, EB_PAGE_SIZE = # buf1 + # buf0 % EB_PAGE_SIZE, avol[n] = mapped(buf0), lpt1[n] = mklp(m3, # buf0, lpf, m4), ¬ isbuf1, keyset(gch) = gc-heap(lpt1, log0), buf1 ≠ mkbuf(0), lpf ≠ LP_FREE, n < # avol, abs-padding(buf1), awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol), bufs-log-only(buffered(n), log0, lpt1), freelist-cons(lpt1, freelist), is-aligned(# buf0, 2 * NODE_HEADER_SIZE), log-group-block(log0, lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, log0), # buf0 ≤ LEB_SIZE, # buf0 + # buf1 ≤ LEB_SIZE, ¬ is-aligned(# buf0, EB_PAGE_SIZE) ⊦ [awbuf_write_buf#(# buf1, buf1, adr, m2, log0, lpt0, ns, buffered(n); avol, isbuf1; err)] ( awbuf-inv(avol, buffered(n)) ∧ # lpt0 = # avol → ⟪m := EB_PAGE_SIZE - lpt1[buffered(n).leb].size % EB_PAGE_SIZE; bleb1 := buffered(n); if err = ESUCCESS then lpt1[bleb1.leb] := mklp(lpt1[bleb1.leb].ref-size, lpt1[bleb1.leb].size + m, lpt1[bleb1.leb].flags, lpt1[bleb1.leb].gcheapidx) else {debug#("persistence: flushing of LEB " + bleb1.leb.toString + " failed"); lpt1[bleb1.leb] := mklp(lpt1[bleb1.leb].ref-size, LEB_SIZE, lpt1[bleb1.leb].flags, lpt1[bleb1.leb].gcheapidx); awbuf_enter_readonly#(adr, m2, log0, avol, lpt0, ns, bleb1; ; isbuf1)}⟫ ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log0) ∧ bufs-log-only(bleb1, log0, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log0, lpt1) ∧ buf-ro-rw-mode(isbuf1, bleb1, lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log0) ∧ awbuf-inv(avol, bleb1)))

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 39:
# lpt0 = # avol, # lpt1 = # avol, isbuf ↔ isbuf1, EB_PAGE_SIZE = # buf1 + # buf0 % EB_PAGE_SIZE, lpt1[n] = mklp(m3, # buf0, lpf, m4), avol[n] = mapped(buf0), bleb = buffered(n), buf = buf1, ¬ isbuf1, keyset(gch) = gc-heap(lpt1, log0), log = log0, lpt = lpt0, m0 = m2, n0 = # buf1, n < # avol, abs-padding(buf1), awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol), bufs-log-only(buffered(n), log0, lpt1), freelist-cons(lpt1, freelist), is-aligned(# buf0, 2 * NODE_HEADER_SIZE), log-group-block(log0, lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log0), # buf0 + # buf1 ≤ LEB_SIZE, # buf0 ≤ LEB_SIZE ⊦ [if bleb ≠ nobuffer ∧ # avol[bleb.leb].data + n0 ≤ LEB_SIZE ∧ n0 ≤ # buf then if isbuf then err := EROFS else {fail_or_success#(; ; err); let m = bleb.leb in if err = ESUCCESS then avol[m] := mapped(avol[m].data + subarray(buf, 0, n0)) else { choose n with n ≠ 0 ∧ n < n0 ∧ is-aligned(# avol[m].data + n, EB_PAGE_SIZE) in avol[m] := mapped(avol[m].data + subarray(buf, 0, n)) ifnone skip or skip; isbuf := true}} else abort] ( awbuf-inv(avol, buffered(n)) ∧ # lpt0 = # avol → ⟪m := EB_PAGE_SIZE - lpt1[buffered(n).leb].size % EB_PAGE_SIZE; bleb1 := buffered(n); isbuf1 := isbuf; if err = ESUCCESS then lpt1[bleb1.leb] := mklp(lpt1[bleb1.leb].ref-size, lpt1[bleb1.leb].size + m, lpt1[bleb1.leb].flags, lpt1[bleb1.leb].gcheapidx) else {debug#("persistence: flushing of LEB " + bleb1.leb.toString + " failed"); lpt1[bleb1.leb] := mklp(lpt1[bleb1.leb].ref-size, LEB_SIZE, lpt1[bleb1.leb].flags, lpt1[bleb1.leb].gcheapidx); awbuf_enter_readonly#(adr, m2, log0, avol, lpt0, ns, bleb1; ; isbuf1)}⟫ ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log0) ∧ bufs-log-only(bleb1, log0, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log0, lpt1) ∧ buf-ro-rw-mode(isbuf1, bleb1, lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log0) ∧ awbuf-inv(avol, bleb1))), buf1 = mkbuf(0), lpf = LP_FREE, is-aligned(# buf0, EB_PAGE_SIZE)

Rule argument

pos: right 1

Additional information

Used simplifier rules: awbuf_write_buf# (N, BUF, WROOTADR, WMAXINO, WLOG, WLPT, WORPHANS, WBUFLEB ; WVOL, AROFS ; ERR ) {if WBUFLEB ≠ nobuffer ∧ # WVOL[WBUFLEB.leb].data + N ≤ LEB_SIZE ∧ N ≤ # BUF then if AROFS then ERR := EROFS else {fail_or_success#(; ; ERR); let LNUM = WBUFLEB.leb in if ERR = ESUCCESS then WVOL[LNUM] := mapped(WVOL[LNUM].data + subarray(BUF, 0, N)) else { choose N0 with N0 ≠ 0 ∧ N0 < N ∧ is-aligned (# WVOL[LNUM].data + N0, EB_PAGE_SIZE) in WVOL[LNUM] := mapped (WVOL[LNUM].data + subarray(BUF, 0, N0)) ifnone skip or skip; AROFS := true}} else abort };