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Proof step 22 from proof refine-read-gnd (previous step)

# lpt = # avol, # lpt0 = # avol, lpt[m0] = mklp(m3, m4, LP_GROUP_NODES, m5), gstore[m0] = groupblock(gndx, lax1 + @(m1, m2) ' + lax0, m3), gnd = gnd0, keyset(gch) = gc-heap(lpt, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, avol[m0].mapped?, ginval < # avol, m0 < # avol, abs-istore(avol, lpt, istore), abs-nodes (avol[m0].data, groupblock(gndx, lax1 + @(m1, m2) ' + lax0, m3).gndlist, groupblock(gndx, lax1 + @(m1, m2) ' + lax0, m3).ladrlist, mklp(m3, m4, LP_GROUP_NODES, m5).size = LEB_SIZE), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(pstate = readonly, bleb, lpt, avol), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), inv(groupblock(gndx, lax1 + @(m1, m2) ' + lax0, m3)), log-group-block(log1, lpt), lpt-free-unref(lpt), lpt-free-unref(lpt0), lpt-leb-size(lpt), lpt-leb-size(lpt0), lpt-ram-flash(lpt, lpt0, log1), m0 ∈ gstore, istore0 ⊑ istore, isbuf → synced(avol), pstate = unbuffered → bleb = nobuffer, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, pstate = unbuffered → isbuf, mklp(m3, m4, LP_GROUP_NODES, m5).size ≠ LEB_SIZE → mklp(m3, m4, LP_GROUP_NODES, m5).size = # avol[m0].data ⊦ ⟪persistence_read_gnd#(@(m0, m1, m2), adr1, m, log1, avol, lpt0, ns0, bleb, pstate = readonly; gnd; err)⟫ ⟨apersistence_read_gnd#(@(m0, m1, m2), adr1, istore, istore0, ginval, gstore, gstore0, log1, m, ns0, pstate, isbuf; gnd0; err0)⟩ ( (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ gnd = gnd0 ∧ err = err0), dups(log1), m0 ∈ ginval

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
# lpt = # avol, # lpt0 = # avol, # gndx = # lax1 + # lax0 + 1, avol[m0] = mapped(buf), lpt[m0] = mklp(m3, m4, LP_GROUP_NODES, m5), gstore[m0] = groupblock(gndx, lax1 + @(m1, m2) ' + lax0, m3), gnd = gnd0, keyset(gch) = gc-heap(lpt, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, m0 < # avol, abs-istore(avol, lpt, istore), abs-nodes(buf, gndx, lax1 + @(m1, m2) ' + lax0, m4 = LEB_SIZE), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(pstate = readonly, bleb, lpt, avol), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), inv(groupblock(gndx, lax1 + @(m1, m2) ' + lax0, m3)), log-group-block(log1, lpt), lpt-free-unref(lpt), lpt-free-unref(lpt0), lpt-leb-size(lpt), lpt-leb-size(lpt0), lpt-ram-flash(lpt, lpt0, log1), m0 ∈ gstore, istore0 ⊑ istore, ¬ dups(log1), ¬ m0 ∈ ginval, isbuf → synced(avol), pstate = unbuffered → bleb = nobuffer, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, pstate = unbuffered → isbuf, m4 ≠ LEB_SIZE → m4 = # buf ⊦ ⟪persistence_read_gnd#(@(m0, m1, m2), adr1, m, log1, avol, lpt0, ns0, bleb, pstate = readonly; gnd; err)⟫ ⟨apersistence_read_gnd#(@(m0, m1, m2), adr1, istore, istore0, ginval, gstore, gstore0, log1, m, ns0, pstate, isbuf; gnd0; err0)⟩ ( (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ gnd = gnd0 ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ mapped(buf).data = buf; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ m +1 = m + 1; (s)% ⊦ #(ladr ' + lax) = (# lax)+1; (s)% ⊦ #(lax + lax0) = # lax + # lax0; (s)%abs-nodes-elems-adr-length: ⊦ abs-nodes(buf, gndx, lax, weak) → # gndx = # lax; (forward) from specification abs-list[encoding-group-node]% ⊦ avol[n].mapped? ↔ (∃ buf. avol[n] = mapped(buf)); (as)% ⊦ mklp(n2, n3, lpf, m).size = n3; (s)% ⊦ groupblock(gndx, lax, m).ladrlist = lax; (s)% ⊦ groupblock(gndx, lax, m).gndlist = gndx; (s)