[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 29 from proof inv-allocate-ind (previous step)

# lpt0 = # avol, # lpt1 = # avol, lpt1[n0] = mklp(0, m1, LP_FREE, m2), keyset(gch) = gc-heap(lpt1, log0), buffered(n0) ≠ bleb, n0 < # avol, awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, bleb, lpt1, avol), bufs-log-only(bleb, log0, lpt1), freelist-cons(lpt1, n0 ' + nx0), 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), synced(avol) ⊦ [awbuf_remap#(n0, adr, m, log0, lpt0, ns, bleb, false; avol; err)] ( awbuf-inv(avol, bleb) ∧ # lpt0 = # avol → ⟪n := n0; freelist := n0 ' + nx0; if err = ESUCCESS then {freelist := freelist.tail; lpt1[n] := mklp(lpt1[n].ref-size, 0, lpt1[n].flags, lpt1[n].gcheapidx); lpt1[n].ref-size := 0}; isbuf1 := false; if err = ESUCCESS then {awbuf_move_buf#(n, 0, adr, m, log0, avol, lpt0, ns, isbuf1; bleb; err); if err ≠ ESUCCESS then freelist := n ' + freelist else lpt1[n].flags := LP_INDEX_NODES}⟫ ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log0) ∧ bufs-log-only(bleb, log0, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log0, lpt1) ∧ buf-ro-rw-mode(isbuf1, bleb, lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log0) ∧ awbuf-inv(avol, bleb)))

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 30:
# lpt1 = # avol, # lpt0 = # avol, isbuf ↔ false, lpt1[n0] = mklp(0, m1, LP_FREE, m2), keyset(gch) = gc-heap(lpt1, log0), log = log0, lpt = lpt0, m0 = n0, n0 < # avol, awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, bleb, lpt1, avol), bufs-log-only(bleb, log0, lpt1), freelist-cons(lpt1, n0 ' + nx0), 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), synced(avol) ⊦ [if synced(avol) ∧ m0 < # avol ∧ buffered(m0) ≠ bleb then {fail_or_success#(; ; err); if err = ESUCCESS then avol[m0] := mapped(mkbuf(0)) else {skip or avol[m0] := unmapped}} else abort] ( awbuf-inv(avol, bleb) ∧ # lpt0 = # avol → ⟪n := n0; freelist := n0 ' + nx0; if err = ESUCCESS then {freelist := freelist.tail; lpt1[n] := mklp(lpt1[n].ref-size, 0, lpt1[n].flags, lpt1[n].gcheapidx); lpt1[n].ref-size := 0}; isbuf1 := false; if err = ESUCCESS then {awbuf_move_buf#(n, 0, adr, m, log0, avol, lpt0, ns, isbuf1; bleb; err); if err ≠ ESUCCESS then freelist := n ' + freelist else lpt1[n].flags := LP_INDEX_NODES}⟫ ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log0) ∧ bufs-log-only(bleb, log0, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log0, lpt1) ∧ buf-ro-rw-mode(isbuf1, bleb, lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log0) ∧ awbuf-inv(avol, bleb))), buffered(n0) = bleb

Rule argument

pos: right 1

Additional information

Used simplifier rules: awbuf_remap# (LNUM, WROOTADR, WMAXINO, WLOG, WLPT, WORPHANS, WBUFLEB, AROFS ; WVOL ; ERR ) {if synced(WVOL) ∧ LNUM < # WVOL ∧ buffered(LNUM) ≠ WBUFLEB then {fail_or_success#(; ; ERR); if ERR = ESUCCESS then WVOL[LNUM] := mapped(mkbuf(0)) else {skip or WVOL[LNUM] := unmapped}} else abort };