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Proof step 9 from proof refine-set-gblock-refsize (previous step)

# lpt = # avol, # lpt0 = # avol, lpt[m] = mklp(m1, m2, LP_GROUP_NODES, m3), gstore[m] = groupblock(gndx, lax, m1), keyset(gch) = gc-heap(lpt, log0), log = log0, remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log0 ∩ ginval = ∅, dom gstore0 ∪ elems log0 = dom gstore ∪ ginval, ginval < # avol, m < # avol, abs-gstore(avol, lpt, gstore, ginval), abs-istore(avol, lpt, istore), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(pstate = readonly, bleb, lpt, avol), bufs-log-only(bleb, log0, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), 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), m ∈ gstore, istore0 ⊑ istore, isbuf → synced(avol), pstate = unbuffered → bleb = nobuffer, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate.journal? → log0 ≠ [] ∧ pstate.lnum = log0.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, pstate = unbuffered → isbuf ⊦ ⟪lpt[m].ref-size := n; if ¬ m ∈ log then gc_heap_update#(lpt[m].gcheapidx, n; gch, lpt)⟫ ⟨apersistence_set_gblock_refsize#(m, n, adr0, istore, istore0, ginval, gstore0, log0, m0, ns0, pstate, isbuf; gstore)⟩ ( abs-istore(avol, lpt, istore) ∧ abs-gstore(avol, lpt, gstore, ginval) ∧ ginval < # lpt ∧ (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum))), dups(log0)

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 10:
# lpt0 = # avol, # lpt1 = # avol, gstore[m] = groupblock(gndx, lax, m1), lpt1[m] = mklp(m1, m2, LP_GROUP_NODES, m3), keyset(gch) = gc-heap(lpt1, log0), log = log0, lpt = lpt1[m, lpt1[m].ref-size:= n], remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log0 ∩ ginval = ∅, dom gstore0 ∪ elems log0 = dom gstore ∪ ginval, m < # avol, ginval < # avol, m < # lpt1, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(pstate = readonly, bleb, lpt1, avol), bufs-log-only(bleb, log0, lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), 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), m ∈ gstore, istore0 ⊑ istore, pstate = unbuffered → isbuf, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log0 ≠ [] ∧ pstate.lnum = log0.last ∧ pstate.lnum ∈ gstore, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate = unbuffered → bleb = nobuffer, isbuf → synced(avol) ⊦ ⟪if ¬ m ∈ log then gc_heap_update#(lpt[m].gcheapidx, n; gch, lpt)⟫ ⟨apersistence_set_gblock_refsize#(m, n, adr0, istore, istore0, ginval, gstore0, log0, m0, ns0, pstate, isbuf; gstore)⟩ ( abs-istore(avol, lpt, istore) ∧ abs-gstore(avol, lpt, gstore, ginval) ∧ ginval < # lpt ∧ (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum))), dups(log0)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ ¬ natkey < natkey; (s)