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Proof step 23 from proof refine-set-gblock-refsize (previous step)

# lpt0 = # avol, # lpt1 = # avol, gstore[m] = groupblock(gndx, lax, m1), lpt1[m] = mklp(m1, m2, LP_GROUP_NODES, m3), adr = adr0, istore = istore1, istore0 = istore2, keyset(gch) = gc-heap(lpt1, log0), keyset(gch0) = (gc-heap(lpt1, log0) -- key-index(m1, m)) ++ key-index(n, m), log = log0, maxino = m0, ns = ns0, remove-refsize0(istore1) = istore1, remove-refsize0(gstore0) = gstore0, elems log0 ∩ ginval = ∅, dom gstore0 ∪ elems log0 = dom gstore ∪ ginval, ginval < # avol, m < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore2), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt1), bin-heap-inv(gch0, lpt2), buf-ro-rw-mode(pstate = readonly, bleb, lpt1, avol), bufs-log-only(bleb, log0, lpt1), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), id-idx(lpt1[m, mklp(n, m2, LP_GROUP_NODES, m3)], lpt2), inv(istore1), inv(istore2), 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), key-index(m1, m) ∈ gc-heap(lpt1, log0), m ∈ gstore, m ∈ gstore0, istore1 ⊑ istore2, pstate = unbuffered → isbuf, pstate.index? → pstate.lnum ∈ istore2, 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) ⊦ # gc-heap(lpt1, log0) = 0, gc-heap(lpt1, log0) = ∅, dups(log0), m ∈ log0, abs-gstore(avol, lpt1[m, mklp(n, m2, LP_GROUP_NODES, m3)], gstore[m, gstore[m].ref-size:= n], ginval) ∧ ginval < # lpt2 ∧ (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
# 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), keyset(gch0) = (gc-heap(lpt1, log0) -- key-index(m1, m)) ++ key-index(n, m), remove-refsize0(istore1) = istore1, remove-refsize0(gstore0) = gstore0, elems log0 ∩ ginval = ∅, dom gstore0 ∪ elems log0 = dom gstore ∪ ginval, ginval < # avol, m < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore2), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt1), bin-heap-inv(gch0, lpt2), buf-ro-rw-mode(pstate = readonly, bleb, lpt1, avol), bufs-log-only(bleb, log0, lpt1), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), id-idx(lpt1[m, mklp(n, m2, LP_GROUP_NODES, m3)], lpt2), inv(istore1), inv(istore2), 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), key-index(m1, m) ∈ gc-heap(lpt1, log0), m ∈ gstore, m ∈ gstore0, istore1 ⊑ istore2, pstate = unbuffered → isbuf, pstate.index? → pstate.lnum ∈ istore2, 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) ⊦ # gc-heap(lpt1, log0) = 0, gc-heap(lpt1, log0) = ∅, ginval < # lpt2, dups(log0), m ∈ log0

Rule argument

Additional information

Used simplifier rules: ⊦ n ∈ gstore ∧ gstore[n] = groupblock(gndx, lax, n3) ∧ abs-gstore(avol, lpt, gstore, ginval) ∧ lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n4) → abs-gstore (avol, lpt[n, mklp(m0, n1, LP_GROUP_NODES, n2)], gstore[n, groupblock(gndx, lax, m0)], ginval); (s)% ⊦ groupblock(gndx, lax, m).ref-size:= m0 = groupblock(gndx, lax, m0); (s)