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Proof step 32 from proof refine-read-gblock-nodes (previous step)

# gndx3 = # lax0, # lpt = # avol, # lpt0 = # avol, avol[m] = mapped(buf), lpt[m] = mklp(m1, m2, LP_GROUP_NODES, m3), gstore2[m] = groupblock(gndx1, lax, m1), err = err1, err = ESUCCESS, keyset(gch) = gc-heap(lpt, log1), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore1) = istore1, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, ginval < # avol, m < # avol, abs-istore(avol, lpt, istore2), abs-leb(mapped(buf), groupblock(gndx1, lax, m1), mklp(m1, m2, LP_GROUP_NODES, m3)), abs-nodes(buf, gndx3, lax0, true), 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, istore1, gstore1), freelist-cons(lpt, freelist), inv(gstore2 \ ginval), inv(gstore1), inv(istore2), inv(istore1), inv(groupblock(gndx1, lax, m1)), 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), m ∈ gstore2, istore1 ⊑ istore2, err1 = ESUCCESS → ax1 = ax0 + lax0.to-adr(m) ∧ gndx2 = gndx0 + gndx3, isbuf → synced(avol), pstate = unbuffered → bleb = nobuffer, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore2, pstate.index? → pstate.lnum ∈ istore2, pstate = unbuffered → isbuf, err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ dups(log1), m ∈ ginval, (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ ax1 = ax0 + gstore2[m].ladrlist.to-adr(m) ∧ gndx2 = gndx0 + gstore2[m].gndlist ∧ err1 = err

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
# gndx3 = # lax0, # lpt = # avol, # lpt0 = # avol, avol[m] = mapped(buf), lpt[m] = mklp(m1, m2, LP_GROUP_NODES, m3), gstore2[m] = groupblock(gndx1, lax, m1), keyset(gch) = gc-heap(lpt, log1), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore1) = istore1, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, ginval < # avol, m < # avol, abs-istore(avol, lpt, istore2), abs-leb(mapped(buf), groupblock(gndx1, lax, m1), mklp(m1, m2, LP_GROUP_NODES, m3)), abs-nodes(buf, gndx3, lax0, true), 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, istore1, gstore1), freelist-cons(lpt, freelist), inv(gstore2 \ ginval), inv(gstore1), inv(istore2), inv(istore1), inv(groupblock(gndx1, lax, m1)), 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), m ∈ gstore2, istore1 ⊑ istore2, isbuf → synced(avol), pstate = unbuffered → bleb = nobuffer, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore2, pstate.index? → pstate.lnum ∈ istore2, pstate = unbuffered → isbuf ⊦ dups(log1), m ∈ ginval, lax0 = lax ∧ gndx3 = gndx1

Rule argument

Additional information

Used simplifier rules: a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ gndx + gndx0 = gndx + gndx1 ↔ gndx0 = gndx1; (s)% ⊦ groupblock(gndx, lax, m).gndlist = gndx; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ lax0.to-adr(n) = lax1.to-adr(n) ↔ lax0 = lax1; (s)% ⊦ ax + ax0 = ax + ax1 ↔ ax0 = ax1; (s)% ⊦ groupblock(gndx, lax, m).ladrlist = lax; (s)