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Proof step 23 from proof refine-read-gnd (previous step)

# 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)

User applied rule apply lemma

And obtained the following new goals

Proof step 24:
⊦ abs-nodes(buf, gndx, lax0 + ladr ' + lax1, boolvar0) → (∃ buf0, buf1, buf2, gndx0, gnd, gndx1. gndx = gndx0 + gnd ' + gndx1 ∧ # gndx0 = # lax0 ∧ buf = buf0 + buf1 + buf2 ∧ ladr = @(# buf0, gnd.flashsize) ∧ # buf1 = gnd.flashsize ∧ abs-node(buf1, gnd))
Proof step 25:
# gndx = # lax1 + # lax0 + 1, # lpt0 = # avol, # lpt = # avol, gstore[m0] = groupblock(gndx, lax1 + @(m1, m2) ' + lax0, m3), lpt[m0] = mklp(m3, m4, LP_GROUP_NODES, m5), avol[m0] = mapped(buf), gnd = gnd0, keyset(gch) = gc-heap(lpt, log1), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, m0 < # avol, ginval < # 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(groupblock(gndx, lax1 + @(m1, m2) ' + lax0, m3)), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt), lpt-free-unref(lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt0), lpt-leb-size(lpt), lpt-ram-flash(lpt, lpt0, log1), m0 ∈ gstore, istore0 ⊑ istore, m4 ≠ LEB_SIZE → m4 = # buf, pstate = unbuffered → isbuf, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate = unbuffered → bleb = nobuffer, isbuf → synced(avol), abs-nodes(buf, gndx, lax1 + @(m1, m2) ' + lax0, m4 = LEB_SIZE) → (∃ buf0, buf1, buf2, gndx0, gnd, gndx1. gndx = gndx0 + gnd ' + gndx1 ∧ # gndx0 = # lax1 ∧ buf = buf0 + buf1 + buf2 ∧ @(m1, m2) = @(# buf0, gnd.flashsize) ∧ # buf1 = gnd.flashsize ∧ abs-node(buf1, gnd)) ⊦ ⟪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

Rule argument

spec: abs-list, inst: encoding-group-node name: abs-split-by-address seq: ⊦ abs-nodes(buf, gndx, lax0 + ladr ' + lax1, boolvar0) → (∃ buf0, buf1, buf2, gndx0, gnd, gndx1. gndx = gndx0 + gnd ' + gndx1 ∧ # gndx0 = # lax0 ∧ buf = buf0 + buf1 + buf2 ∧ ladr = @(# buf0, gnd.flashsize) ∧ # buf1 = gnd.flashsize ∧ abs-node(buf1, gnd)) subst: [buf, gndx, lax0, ladr, lax1, boolvar0] → [buf, gndx, lax1, @(m1, m2), lax0, m4 = LEB_SIZE]

Additional information

Used terms: buf, gndx, lax1, @(m1, m2), lax0, m4 = LEB_SIZE