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Proof step 115 from proof refine-add-gnds (previous step)

# lpt1 = # avol, # lpt0 = # avol, # buf0 = gndx0.flashsize, # gndx0 = # lax0, (elems nx ∪ dom gstore0) ++ n = dom gstore ∪ ginval, gstore[n] = groupblock(gndx, lax, m0), lpt1[n] = mklp(m0, # buf, LP_GROUP_NODES, m2), avol[n] = mapped(buf), ¬ isbuf2, keyset(gch) = gc-heap(lpt1, nx + n '), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, ginval ∩ elems nx = ∅, gndx0 ≠ [], ginval < # avol, n < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), abs-nodes(buf0, # buf, gndx0, lax0, 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), nx + n ', lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(groupblock(gndx, lax, m0)), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(nx + n ', lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, nx + n '), n ∈ gstore, # buf + gndx0.flashsize ≤ LEB_SIZE, istore0 ⊑ istore, ¬ dups(nx), ¬ n ∈ nx, ¬ n ∈ ginval, isbuf1 → synced(avol) ⊦ [awbuf_write_buf#(gndx0.flashsize, buf0, adr0, m, nx + n ', lpt0, ns0, buffered((nx + n ').last); avol, isbuf2; err); log1 := nx + n '; if err = ESUCCESS then lpt1[buffered(log1.last).leb] := mklp (lpt1[buffered(log1.last).leb].ref-size, lpt1[buffered(log1.last).leb].size + gndx0.flashsize, lpt1[buffered(log1.last).leb].flags, lpt1[buffered(log1.last).leb].gcheapidx) else {debug#("persistence: adding group node to LEB " + buffered(log1.last).leb.toString + " failed"); lpt1[buffered(log1.last).leb] := mklp(lpt1[buffered(log1.last).leb].ref-size, LEB_SIZE, lpt1[buffered(log1.last).leb].flags, lpt1[buffered(log1.last).leb].gcheapidx)}] ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log1) ∧ bufs-log-only(buffered(n), log1, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log1, lpt1) ∧ buf-ro-rw-mode(isbuf2, buffered(n), lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log1) ∧ awbuf-inv(avol, buffered(n)) ∧ # lpt0 = # avol → ⟨pstate := journal(log1.last); apersistence_add_gnds#(gndx0, adr0, istore, istore0, ginval, gstore0, log1, m, ns0; ax0, gstore, pstate, isbuf1; err0)⟩ ( abs-istore(avol, lpt1, istore) ∧ abs-gstore(avol, lpt1, gstore, ginval) ∧ ginval < # lpt1 ∧ (isbuf1 → synced(avol)) ∧ pstate ≠ unbuffered ∧ (pstate = readonly ↔ isbuf2) ∧ (pstate ≠ readonly → n = pstate.lnum) ∧ lax0.to-adr(n) = ax0 ∧ err = err0))

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 116:
# gndx0 = # lax0, # buf0 = gndx0.flashsize, # lpt0 = # avol, # lpt1 = # avol, (elems nx ∪ dom gstore0) ++ n = dom gstore ∪ ginval, isbuf ↔ isbuf2, avol[n] = mapped(buf1), lpt1[n] = mklp(m1, # buf1, LP_GROUP_NODES, m2), gstore[n] = groupblock(gndx, lax, m1), adr = adr0, bleb = buffered((nx + n ').last), buf = buf0, ¬ isbuf2, keyset(gch) = gc-heap(lpt1, nx + n '), log = nx + n ', lpt = lpt0, m0 = m, n0 = gndx0.flashsize, ns = ns0, remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, ginval ∩ elems nx = ∅, n < # avol, ginval < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), abs-nodes(buf0, # buf1, gndx0, lax0, 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), nx + n ', lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), inv(groupblock(gndx, lax, m1)), log-group-block(nx + n ', lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, nx + n '), n ∈ gstore, # buf1 + gndx0.flashsize ≤ LEB_SIZE, istore0 ⊑ istore, isbuf1 → synced(avol) ⊦ [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; log1 := nx + n '; if err = ESUCCESS then lpt1[buffered(log1.last).leb] := mklp (lpt1[buffered(log1.last).leb].ref-size, lpt1[buffered(log1.last).leb].size + gndx0.flashsize, lpt1[buffered(log1.last).leb].flags, lpt1[buffered(log1.last).leb].gcheapidx) else {debug#("persistence: adding group node to LEB " + buffered(log1.last).leb.toString + " failed"); lpt1[buffered(log1.last).leb] := mklp(lpt1[buffered(log1.last).leb].ref-size, LEB_SIZE, lpt1[buffered(log1.last).leb].flags, lpt1[buffered(log1.last).leb].gcheapidx)}] ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log1) ∧ bufs-log-only(buffered(n), log1, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log1, lpt1) ∧ buf-ro-rw-mode(isbuf, buffered(n), lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log1) ∧ awbuf-inv(avol, buffered(n)) ∧ # lpt0 = # avol → ⟨pstate := journal(log1.last); apersistence_add_gnds#(gndx0, adr0, istore, istore0, ginval, gstore0, log1, m, ns0; ax0, gstore, pstate, isbuf1; err0)⟩ ( abs-istore(avol, lpt1, istore) ∧ abs-gstore(avol, lpt1, gstore, ginval) ∧ ginval < # lpt1 ∧ (isbuf1 → synced(avol)) ∧ pstate ≠ unbuffered ∧ (pstate = readonly ↔ isbuf) ∧ (pstate ≠ readonly → n = pstate.lnum) ∧ lax0.to-adr(n) = ax0 ∧ err = err0)), nx + n ' = [], gndx0 = [], dups(nx), n ∈ nx, n ∈ ginval

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 };