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Proof step 47 from proof inv-allocate-gnd (previous step)

# lpt1 = # avol0, # lpt0 = # avol0, # lpt0 = # avol, lpt1[n0] = mklp(0, m1, LP_FREE, m2), avol = avol0[n0, mapped(mkbuf(0))], err = ESUCCESS, err = err0, freelist = n0 ' + nx0, keyset(gch) = gc-heap(lpt1, log1), n = n0, n0 < # avol0, awbuf-inv(avol0, bleb), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, bleb, lpt1, avol0), bufs-log-only(bleb, log1, lpt1), freelist-cons(lpt1, n0 ' + nx0), log-group-block(log1, lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log1), synced(avol0), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟪freelist := freelist.tail; lpt1[n] := mklp(lpt1[n].ref-size, 0, lpt1[n].flags, lpt1[n].gcheapidx); lpt1[n].ref-size := 0; log := log1; isbuf1 := false; if err = ESUCCESS then {awbuf_add_log_leb#(n, 0, adr, m, avol, lpt0, ns, isbuf1; log, bleb; err); if err ≠ ESUCCESS then freelist := n ' + freelist}; if err = ESUCCESS then {lpt1[n].flags := LP_GROUP_NODES; log1 := log1 + n '}⟫ ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ log1 = log ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log) ∧ bufs-log-only(bleb, log, lpt1) ∧ # lpt1 = # avol ∧ ¬ dups(log) ∧ log-group-block(log, lpt1) ∧ buf-ro-rw-mode(isbuf1, bleb, lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log) ∧ awbuf-inv(avol, bleb)), buffered(n0) = bleb, dups(log1)

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 48:
# lpt0 = # avol, # lpt0 = # avol0, # lpt1 = # avol0, lpt1[n0] = mklp(0, m1, LP_FREE, m2), avol = avol0[n0, mapped(mkbuf(0))], err = err0, err = ESUCCESS, freelist = freelist0.tail, freelist0 = n0 ' + nx0, keyset(gch) = gc-heap(lpt1, log1), n = n0, n0 < # avol0, awbuf-inv(avol, bleb), awbuf-inv(avol0, bleb), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, bleb, lpt1, avol0), bufs-log-only(bleb, log1, lpt1), freelist-cons(lpt1, n0 ' + nx0), log-group-block(log1, lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, log1), synced(avol0), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟪lpt1[n] := mklp(lpt1[n].ref-size, 0, lpt1[n].flags, lpt1[n].gcheapidx); lpt1[n].ref-size := 0; log := log1; isbuf1 := false; if err = ESUCCESS then {awbuf_add_log_leb#(n, 0, adr, m, avol, lpt0, ns, isbuf1; log, bleb; err); if err ≠ ESUCCESS then freelist := n ' + freelist}; if err = ESUCCESS then {lpt1[n].flags := LP_GROUP_NODES; log1 := log1 + n '}⟫ ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ log1 = log ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log) ∧ bufs-log-only(bleb, log, lpt1) ∧ # lpt1 = # avol ∧ ¬ dups(log) ∧ log-group-block(log, lpt1) ∧ buf-ro-rw-mode(isbuf1, bleb, lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log) ∧ awbuf-inv(avol, bleb)), buffered(n0) = bleb, freelist0 = [], dups(log1)

Rule argument

Additional information

Used simplifier rules: ⊦ nx + nx0 = [] ↔ nx = [] ∧ nx0 = []; (as)% ⊦ n ' ≠ []; (s)%a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]