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Proof step 33 from proof inv-allocate-gnd (previous step)

# lpt0 = # avol, # lpt1 = # avol, lpt1[n0] = mklp(0, m1, LP_FREE, m2), keyset(gch) = gc-heap(lpt1, log1), n0 < # avol, awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, bleb, lpt1, avol), 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(avol), ¬ dups(log1) ⊦ ⟪awbuf_remap#(n0, adr, m, log1, lpt0, ns, bleb, false; avol; err); 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}; 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) ∧ # lpt0 = # avol)

User applied rule insert program lemma

And obtained the following new goals

Proof step 34:
awbuf-inv(avol, bleb), # lpt = # avol, synced(avol), m < # avol, buffered(m) ≠ bleb ⊦ ⟪awbuf_remap#(m, adr, m0, nx, lpt, ns, bleb, isbuf; avol; err)⟫ (awbuf-inv(avol, bleb) ∧ # lpt = # avol)
Proof step 35:
# lpt1 = # avol, # lpt0 = # avol, isbuf0 ↔ false, lpt1[n0] = mklp(0, m1, LP_FREE, m2), adr0 = adr, bleb0 = bleb, keyset(gch) = gc-heap(lpt1, log1), lpt2 = lpt0, m3 = n0, m4 = m, ns0 = ns, nx1 = log1, n0 < # avol, awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, bleb, lpt1, avol), 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(avol) ⊦ [awbuf_remap#(n0, adr, m, log1, lpt0, ns, bleb, false; avol; err)] ( awbuf-inv(avol, bleb0) ∧ # lpt2 = # 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}; 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) ∧ # lpt0 = # avol)), buffered(n0) = bleb, dups(log1)

Rule argument

spec: awbuf-asm name: inv-remap seq: awbuf-inv(avol, bleb), # lpt = # avol, synced(avol), m < # avol, buffered(m) ≠ bleb ⊦ ⟪awbuf_remap# (m, adr, m0, nx, lpt, ns, bleb, isbuf; avol; err)⟫ (awbuf-inv(avol, bleb) ∧ # lpt = # avol) subst: [isbuf, bleb, ns, lpt, nx, m0, adr, m, avol, err] → [false, bleb, ns, lpt0, log1, m, adr, n0, avol, err] flags: <all paths>

Additional information

Used simplifier rules: ⊦ lpt[n] = mklp(n0, n1, LP_FREE, n2) → ¬ bufs-log-only(buffered(n), freelist, lpt); (s)