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Proof step 41 from proof inv-add-gnds (previous step)

# gndx = # lax, # buf0 = gndx.flashsize, # lpt1 = # avol, # lpt0 = # avol, avol[n] = mapped(buf), lpt1[n] = mklp(m4, # buf, LP_GROUP_NODES, m2), adr0 = adr, bleb0 = buffered(n), buf1 = buf0, ¬ isbuf1, keyset(gch) = gc-heap(lpt1, log0), lpt2 = lpt0, m0 = m, n0 = gndx.flashsize, ns0 = ns, nx0 = log0, n < # avol, abs-nodes(buf0, # buf, gndx, lax, false), awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol), bufs-log-only(buffered(n), log0, lpt1), freelist-cons(lpt1, freelist), 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), n ∈ log0, # buf + gndx.flashsize ≤ LEB_SIZE, # avol[buffered(n).leb].data + gndx.flashsize ≤ LEB_SIZE, gndx.flashsize ≤ # buf0 ⊦ [awbuf_write_buf#(gndx.flashsize, buf0, adr, m, log0, lpt0, ns, buffered(n); avol, isbuf1; err)] ( awbuf-inv(avol, bleb0) ∧ # lpt2 = # avol → ⟪if err = ESUCCESS then lpt1[buffered(n).leb] := mklp (lpt1[buffered(n).leb].ref-size, lpt1[buffered(n).leb].size + gndx.flashsize, lpt1[buffered(n).leb].flags, lpt1[buffered(n).leb].gcheapidx) else {debug#("persistence: adding group node to LEB " + buffered(n).leb.toString + " failed"); lpt1[buffered(n).leb] := mklp(lpt1[buffered(n).leb].ref-size, LEB_SIZE, lpt1[buffered(n).leb].flags, lpt1[buffered(n).leb].gcheapidx)}⟫ ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log0) ∧ bufs-log-only(buffered(n), log0, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log0, lpt1) ∧ buf-ro-rw-mode(isbuf1, buffered(n), lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log0) ∧ awbuf-inv(avol, buffered(n)) ∧ # lpt0 = # avol)), buffered(n) = nobuffer, gndx = [], dups(log0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
# gndx = # lax, # buf0 = gndx.flashsize, # lpt1 = # avol, # lpt0 = # avol, avol[n] = mapped(buf), lpt1[n] = mklp(m4, # buf, LP_GROUP_NODES, m2), ¬ isbuf1, keyset(gch) = gc-heap(lpt1, log0), gndx ≠ [], n < # avol, abs-nodes(buf0, # buf, gndx, lax, false), awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol), bufs-log-only(buffered(n), log0, lpt1), freelist-cons(lpt1, freelist), 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), n ∈ log0, # buf + gndx.flashsize ≤ LEB_SIZE, ¬ dups(log0) ⊦ [awbuf_write_buf#(gndx.flashsize, buf0, adr, m, log0, lpt0, ns, buffered(n); avol, isbuf1; err)] ( awbuf-inv(avol, buffered(n)) ∧ # lpt0 = # avol → ⟪if err = ESUCCESS then lpt1[buffered(n).leb] := mklp (lpt1[buffered(n).leb].ref-size, lpt1[buffered(n).leb].size + gndx.flashsize, lpt1[buffered(n).leb].flags, lpt1[buffered(n).leb].gcheapidx) else {debug#("persistence: adding group node to LEB " + buffered(n).leb.toString + " failed"); lpt1[buffered(n).leb] := mklp(lpt1[buffered(n).leb].ref-size, LEB_SIZE, lpt1[buffered(n).leb].flags, lpt1[buffered(n).leb].gcheapidx)}⟫ ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log0) ∧ bufs-log-only(buffered(n), log0, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log0, lpt1) ∧ buf-ro-rw-mode(isbuf1, buffered(n), lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log0)))

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ buffered(m).leb = m; (s)% ⊦ nobuffer ≠ buffered(m); (s)