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Proof step 28 from proof refine-add-gnds (previous step)

# lpt = # avol, # lpt0 = # avol, pstate = readonly ↔ isbuf0, lpt[bleb.leb] = mklp(m3, m1, lpf, m2), adr = adr0, ax = ax0, bleb0 = bleb, gndx = gndx0, keyset(gch) = gc-heap(lpt, log1), log = log1, log0 = log1, m0 = LEB_SIZE, ns = ns0, remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, abs-gstore(avol, lpt, gstore, ginval), abs-istore(avol, lpt, istore), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(pstate = readonly, bleb, lpt, avol), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt), lpt-free-unref(lpt), lpt-free-unref(lpt0), lpt-leb-size(lpt), lpt-leb-size(lpt0), lpt-ram-flash(lpt, lpt0, log1), istore0 ⊑ istore, pstate = unbuffered → isbuf1, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate = unbuffered → bleb = nobuffer, isbuf1 → synced(avol), pstate ≠ readonly → bleb.isbuf? ∧ bleb.leb < # avol ∧ lpf = LP_GROUP_NODES ∧ bleb.leb ∈ log1 ∧ avol[bleb.leb].mapped? ∧ (gndx0 ≠ [] ∧ m1 + gndx0.flashsize ≤ LEB_SIZE → m1 = # avol[bleb.leb].data), pstate.journal? ∨ pstate = readonly ⊦ [awbuf_is_readonly#(adr, m, log, avol, lpt0, ns, bleb0, isbuf0; ; isbuf); if isbuf then err := EROFS else if gndx = [] then {ax := []; err := ESUCCESS} else let buf = ?, bleb = ? in {awbuf_get_buf#(adr, m, log, avol, lpt0, ns, bleb0, isbuf0; ; bleb); persistence_encode_group_nodes#(gndx, bleb.leb, lpt[bleb.leb].size; ; buf, ax, err); if err = ESUCCESS then if ¬ lpt[bleb.leb].size + # buf ≤ m0 then {debug#("persistence: trying to write beyond LEB size"); awbuf_enter_readonly#(adr, m, log, avol, lpt0, ns, bleb0; ; isbuf0); err := ENOSPC} else {awbuf_write_buf#(# buf, buf, adr, m, log, lpt0, ns, bleb0; avol, isbuf0; err); if err = ESUCCESS then lpt[bleb.leb].size := lpt[bleb.leb].size + # buf else {debug#("persistence: adding group node to LEB " + bleb.leb.toString + " failed"); lpt[bleb.leb].size := m0}} else {debug#("persistence: could not encode group node"); awbuf_enter_readonly#(adr, m, log, avol, lpt0, ns, bleb0; ; isbuf0)}}] ( lpt-free-unref(lpt) ∧ freelist-cons(lpt, freelist) ∧ bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt, log1) ∧ bufs-log-only(bleb, log1, lpt) ∧ # lpt = # avol ∧ log-group-block(log1, lpt) ∧ buf-ro-rw-mode(isbuf0, bleb, lpt, avol) ∧ lpt-leb-size(lpt) ∧ lpt-ram-flash(lpt, lpt0, log1) ∧ awbuf-inv(avol, bleb) ∧ # lpt0 = # avol → ⟨apersistence_add_gnds#(gndx0, adr0, istore, istore0, ginval, gstore0, log1, m, ns0; ax0, gstore, pstate, isbuf1; err0)⟩ ( abs-istore(avol, lpt, istore) ∧ abs-gstore(avol, lpt, gstore, ginval) ∧ ginval < # lpt ∧ (isbuf1 → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate = readonly ↔ isbuf0) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ ax = ax0 ∧ err = err0)), dups(log1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
# lpt0 = # avol, # lpt = # avol, lpt[bleb.leb] = mklp(m3, m1, lpf, m2), keyset(gch) = gc-heap(lpt, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, abs-gstore(avol, lpt, gstore, ginval), abs-istore(avol, lpt, istore), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(pstate = readonly, bleb, lpt, avol), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(log1, lpt), lpt-free-unref(lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt0), lpt-leb-size(lpt), lpt-ram-flash(lpt, lpt0, log1), istore0 ⊑ istore, ¬ dups(log1), pstate ≠ readonly → bleb.isbuf? ∧ bleb.leb < # avol ∧ lpf = LP_GROUP_NODES ∧ bleb.leb ∈ log1 ∧ avol[bleb.leb].mapped? ∧ (gndx0 ≠ [] ∧ m1 + gndx0.flashsize ≤ LEB_SIZE → m1 = # avol[bleb.leb].data), isbuf1 → synced(avol), pstate = unbuffered → bleb = nobuffer, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, pstate = unbuffered → isbuf1, pstate.journal? ∨ pstate = readonly ⊦ [awbuf_is_readonly#(adr0, m, log1, avol, lpt0, ns0, bleb, pstate = readonly; ; isbuf); ax := ax0; isbuf0 := pstate = readonly; if isbuf then err := EROFS else if gndx0 = [] then {ax := []; err := ESUCCESS} else let buf = ?, bleb1 = ? in {awbuf_get_buf#(adr0, m, log1, avol, lpt0, ns0, bleb, isbuf0; ; bleb1); persistence_encode_group_nodes#(gndx0, bleb1.leb, lpt[bleb1.leb].size; ; buf, ax, err); if err = ESUCCESS then if ¬ lpt[bleb1.leb].size + # buf ≤ LEB_SIZE then {debug#("persistence: trying to write beyond LEB size"); awbuf_enter_readonly#(adr0, m, log1, avol, lpt0, ns0, bleb; ; isbuf0); err := ENOSPC} else {awbuf_write_buf#(# buf, buf, adr0, m, log1, lpt0, ns0, bleb; avol, isbuf0; err); if err = ESUCCESS then lpt[bleb1.leb] := mklp(lpt[bleb1.leb].ref-size, lpt[bleb1.leb].size + # buf, lpt[bleb1.leb].flags, lpt[bleb1.leb].gcheapidx) else {debug#("persistence: adding group node to LEB " + bleb1.leb.toString + " failed"); lpt[bleb1.leb] := mklp(lpt[bleb1.leb].ref-size, LEB_SIZE, lpt[bleb1.leb].flags, lpt[bleb1.leb].gcheapidx)}} else {debug#("persistence: could not encode group node"); awbuf_enter_readonly#(adr0, m, log1, avol, lpt0, ns0, bleb; ; isbuf0)}}] ( lpt-free-unref(lpt) ∧ freelist-cons(lpt, freelist) ∧ bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt, log1) ∧ bufs-log-only(bleb, log1, lpt) ∧ # lpt = # avol ∧ log-group-block(log1, lpt) ∧ buf-ro-rw-mode(isbuf0, bleb, lpt, avol) ∧ lpt-leb-size(lpt) ∧ lpt-ram-flash(lpt, lpt0, log1) ∧ awbuf-inv(avol, bleb) ∧ # lpt0 = # avol → ⟨apersistence_add_gnds#(gndx0, adr0, istore, istore0, ginval, gstore0, log1, m, ns0; ax0, gstore, pstate, isbuf1; err0)⟩ ( abs-istore(avol, lpt, istore) ∧ abs-gstore(avol, lpt, gstore, ginval) ∧ ginval < # lpt ∧ (isbuf1 → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate = readonly ↔ isbuf0) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ ax = ax0 ∧ err = err0))

Rule argument

Additional information

Used simplifier rules: ⊦ lp.size:= n = mklp(lp.ref-size, n, lp.flags, lp.gcheapidx); (s)