[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 6 from proof inv-add-gnds (previous step)

# lpt0 = # avol, # lpt = # avol, isbuf0 ↔ isbuf, lpt[bleb.leb] = mklp(m4, m1, lpf, m2), bleb0 = bleb, keyset(gch) = gc-heap(lpt, log0), log = log0, m = m3, m0 = LEB_SIZE, awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(isbuf, bleb, lpt, avol), bufs-log-only(bleb, log0, lpt), freelist-cons(lpt, freelist), log-group-block(log0, lpt), lpt-free-unref(lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt0), lpt-leb-size(lpt), lpt-ram-flash(lpt, lpt0, log0), ¬ isbuf → bleb.isbuf? ∧ bleb.leb < # avol ∧ lpf = LP_GROUP_NODES ∧ bleb.leb ∈ log0 ∧ avol[bleb.leb].mapped? ∧ (gndx ≠ [] ∧ m1 + gndx.flashsize ≤ LEB_SIZE → m1 = # avol[bleb.leb].data) ⊦ ⟪if ¬ isbuf0 → bleb0.isbuf? ∧ bleb0.leb < # lpt ∧ lpt[bleb0.leb].flags = LP_GROUP_NODES ∧ bleb0.leb ∈ log0 ∧ avol[bleb0.leb].mapped? ∧ (gndx ≠ [] ∧ lpt[bleb0.leb].size + gndx.flashsize ≤ LEB_SIZE → lpt[bleb0.leb].size = # avol[bleb0.leb].data) then let isbuf = ? in {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)}}} else abort⟫ ( lpt-free-unref(lpt) ∧ freelist-cons(lpt, freelist) ∧ bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt, log0) ∧ bufs-log-only(bleb, log0, lpt) ∧ # lpt = # avol ∧ log-group-block(log0, lpt) ∧ buf-ro-rw-mode(isbuf0, bleb, lpt, avol) ∧ lpt-leb-size(lpt) ∧ lpt-ram-flash(lpt, lpt0, log0) ∧ awbuf-inv(avol, bleb) ∧ # lpt0 = # avol), dups(log0)

Heuristic conditional right split applied rule if positive right

And obtained the following new goals

Proof step 7:
# lpt = # avol, # lpt0 = # avol, isbuf0 ↔ isbuf, lpt[bleb.leb] = mklp(m4, m1, lpf, m2), bleb0 = bleb, keyset(gch) = gc-heap(lpt, log0), log = log0, m = m3, m0 = LEB_SIZE, awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(isbuf, bleb, lpt, avol), bufs-log-only(bleb, log0, lpt), freelist-cons(lpt, freelist), log-group-block(log0, lpt), lpt-free-unref(lpt), lpt-free-unref(lpt0), lpt-leb-size(lpt), lpt-leb-size(lpt0), lpt-ram-flash(lpt, lpt0, log0), ¬ isbuf → bleb.isbuf? ∧ bleb.leb < # avol ∧ lpf = LP_GROUP_NODES ∧ bleb.leb ∈ log0 ∧ avol[bleb.leb].mapped? ∧ (gndx ≠ [] ∧ m1 + gndx.flashsize ≤ LEB_SIZE → m1 = # avol[bleb.leb].data) ⊦ ⟪let isbuf = ? in {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, log0) ∧ bufs-log-only(bleb, log0, lpt) ∧ # lpt = # avol ∧ log-group-block(log0, lpt) ∧ buf-ro-rw-mode(isbuf0, bleb, lpt, avol) ∧ lpt-leb-size(lpt) ∧ lpt-ram-flash(lpt, lpt0, log0) ∧ awbuf-inv(avol, bleb) ∧ # lpt0 = # avol), dups(log0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)% ⊦ mklp(n2, n3, lpf, m).size = n3; (s)