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Proof step 42 from proof inv-add-gnds (previous step)

# gndx = # lax, # buf0 = gndx.flashsize, # lpt1 = # avol, # lpt0 = # avol, avol[n] = mapped(buf), lpt1[n] = mklp(m4, # buf, LP_GROUP_NODES, m2), ¬ isbuf1, keyset(gch) = gc-heap(lpt1, log0), gndx ≠ [], n < # avol, abs-nodes(buf0, # buf, gndx, lax, false), 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), 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), n ∈ log0, # buf + gndx.flashsize ≤ LEB_SIZE, ¬ dups(log0) ⊦ [awbuf_write_buf#(gndx.flashsize, buf0, adr, m, log0, lpt0, ns, buffered(n); avol, isbuf1; err)] ( awbuf-inv(avol, buffered(n)) ∧ # lpt0 = # avol → ⟪if err = ESUCCESS then lpt1[buffered(n).leb] := mklp (lpt1[buffered(n).leb].ref-size, lpt1[buffered(n).leb].size + gndx.flashsize, lpt1[buffered(n).leb].flags, lpt1[buffered(n).leb].gcheapidx) else {debug#("persistence: adding group node to LEB " + buffered(n).leb.toString + " failed"); lpt1[buffered(n).leb] := mklp(lpt1[buffered(n).leb].ref-size, LEB_SIZE, lpt1[buffered(n).leb].flags, lpt1[buffered(n).leb].gcheapidx)}⟫ ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log0) ∧ bufs-log-only(buffered(n), log0, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log0, lpt1) ∧ buf-ro-rw-mode(isbuf1, buffered(n), lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log0)))

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 43:
# lpt0 = # avol, # lpt1 = # avol, # buf0 = gndx.flashsize, # gndx = # lax, isbuf ↔ isbuf1, lpt1[n] = mklp(m4, # buf1, LP_GROUP_NODES, m2), avol[n] = mapped(buf1), bleb = buffered(n), buf = buf0, ¬ isbuf1, keyset(gch) = gc-heap(lpt1, log0), log = log0, lpt = lpt0, m0 = m, n0 = gndx.flashsize, n < # avol, abs-nodes(buf0, # buf1, gndx, lax, false), 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), 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), n ∈ log0, # buf1 + gndx.flashsize ≤ 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 → ⟪if err = ESUCCESS then lpt1[buffered(n).leb] := mklp (lpt1[buffered(n).leb].ref-size, lpt1[buffered(n).leb].size + gndx.flashsize, lpt1[buffered(n).leb].flags, lpt1[buffered(n).leb].gcheapidx) else {debug#("persistence: adding group node to LEB " + buffered(n).leb.toString + " failed"); lpt1[buffered(n).leb] := mklp(lpt1[buffered(n).leb].ref-size, LEB_SIZE, lpt1[buffered(n).leb].flags, lpt1[buffered(n).leb].gcheapidx)}⟫ ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log0) ∧ bufs-log-only(buffered(n), log0, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log0, lpt1) ∧ buf-ro-rw-mode(isbuf, buffered(n), lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log0))), gndx = [], dups(log0)

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 };