[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 9 from proof inv-sync (previous step)

# lpt = # avol, # lpt0 = # avol, isbuf0 ↔ isbuf1, lpt[bleb1.leb] = mklp(m, m5, lpf, m4), bleb0 = bleb1, keyset(gch) = gc-heap(lpt, log0), log = log0, m2 = m0, m3 = LEB_SIZE, awbuf-inv(avol, bleb1), bin-heap-inv(gch, lpt), buf-ro-rw-mode(isbuf1, bleb1, lpt, avol), bufs-log-only(bleb1, 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), bleb1.isbuf? ∧ ¬ isbuf1 → bleb1.leb < # avol ∧ # avol[bleb1.leb].data ≤ LEB_SIZE ∧ avol[bleb1.leb].mapped? ∧ m5 = # avol[bleb1.leb].data ∧ lpf ≠ LP_FREE ∧ is-aligned(# avol[bleb1.leb].data, 2 * NODE_HEADER_SIZE) ⊦ ⟪awbuf_get_buf#(adr, m2, log, avol, lpt0, ns, bleb0, isbuf0; ; bleb); awbuf_is_readonly#(adr, m2, log, avol, lpt0, ns, bleb0, isbuf0; ; isbuf); awbuf_get_page_size#(adr, m2, log, avol, lpt0, ns, bleb0, isbuf0; ; m1); if ¬ isbuf then if bleb.isbuf? then let m0 = lpt[bleb.leb].size in if ¬ is-aligned(m0, m1) then let m = m1 - m0 % m1 in let buf = mkbuf(m) in {persistence_encode_padding_node#(; buf; err); if err = ESUCCESS then {awbuf_write_buf#(# buf, buf, adr, m2, log, lpt0, ns, bleb0; avol, isbuf0; err); if err = ESUCCESS then lpt[bleb.leb].size := lpt[bleb.leb].size + m else {debug#("persistence: flushing of LEB " + bleb.leb.toString + " failed"); lpt[bleb.leb].size := m3; awbuf_enter_readonly#(adr, m2, log, avol, lpt0, ns, bleb0; ; isbuf0)}} else {debug#("persistence: could not encode padding node"); awbuf_enter_readonly#(adr, m2, log, avol, lpt0, ns, bleb0; ; isbuf0)}} else err := EROFS⟫ ( lpt-free-unref(lpt) ∧ freelist-cons(lpt, freelist) ∧ bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt, log0) ∧ bufs-log-only(bleb1, log0, lpt) ∧ # lpt = # avol ∧ log-group-block(log0, lpt) ∧ buf-ro-rw-mode(isbuf0, bleb1, lpt, avol) ∧ lpt-leb-size(lpt) ∧ lpt-ram-flash(lpt, lpt0, log0) ∧ awbuf-inv(avol, bleb1) ∧ # lpt0 = # avol)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
# lpt0 = # avol, # lpt = # avol, lpt[bleb1.leb] = mklp(m, m5, lpf, m4), keyset(gch) = gc-heap(lpt, log0), awbuf-inv(avol, bleb1), bin-heap-inv(gch, lpt), buf-ro-rw-mode(isbuf1, bleb1, lpt, avol), bufs-log-only(bleb1, 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), bleb1.isbuf? ∧ ¬ isbuf1 → bleb1.leb < # avol ∧ # avol[bleb1.leb].data ≤ LEB_SIZE ∧ avol[bleb1.leb].mapped? ∧ m5 = # avol[bleb1.leb].data ∧ lpf ≠ LP_FREE ∧ is-aligned(# avol[bleb1.leb].data, 2 * NODE_HEADER_SIZE) ⊦ ⟪awbuf_get_buf#(adr, m2, log0, avol, lpt0, ns, bleb1, isbuf1; ; bleb); awbuf_is_readonly#(adr, m2, log0, avol, lpt0, ns, bleb1, isbuf1; ; isbuf); awbuf_get_page_size#(adr, m2, log0, avol, lpt0, ns, bleb1, isbuf1; ; m1); if ¬ isbuf then if bleb.isbuf? then let m0 = lpt[bleb.leb].size in if ¬ is-aligned(m0, m1) then let m = m1 - m0 % m1 in let buf = mkbuf(m) in {persistence_encode_padding_node#(; buf; err); if err = ESUCCESS then {awbuf_write_buf#(# buf, buf, adr, m2, log0, lpt0, ns, bleb1; avol, isbuf1; err); if err = ESUCCESS then lpt[bleb.leb] := mklp(lpt[bleb.leb].ref-size, lpt[bleb.leb].size + m, lpt[bleb.leb].flags, lpt[bleb.leb].gcheapidx) else {debug#("persistence: flushing of LEB " + bleb.leb.toString + " failed"); lpt[bleb.leb] := mklp(lpt[bleb.leb].ref-size, LEB_SIZE, lpt[bleb.leb].flags, lpt[bleb.leb].gcheapidx); awbuf_enter_readonly#(adr, m2, log0, avol, lpt0, ns, bleb1; ; isbuf1)}} else {debug#("persistence: could not encode padding node"); awbuf_enter_readonly#(adr, m2, log0, avol, lpt0, ns, bleb1; ; isbuf1)}} else err := EROFS⟫ ( lpt-free-unref(lpt) ∧ freelist-cons(lpt, freelist) ∧ bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt, log0) ∧ bufs-log-only(bleb1, log0, lpt) ∧ # lpt = # avol ∧ log-group-block(log0, lpt) ∧ buf-ro-rw-mode(isbuf1, bleb1, lpt, avol) ∧ lpt-leb-size(lpt) ∧ lpt-ram-flash(lpt, lpt0, log0) ∧ awbuf-inv(avol, bleb1) ∧ # lpt0 = # avol)

Rule argument

Additional information

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