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Proof step 131 from proof refine-allocate-ind (previous step)

# lpt2 = # avol0, # lpt0 = # avol0, avol0[pstate.lnum] = unmapped, lpt2[n0] = mklp(0, m5, LP_FREE, m6), keyset(gch) = gc-heap(lpt2, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, pstate.lnum < # avol0, ginval < # avol0, n0 < # avol0, abs-gstore(avol0, lpt2, gstore, ginval), abs-istore(avol0, lpt2, istore), awbuf-inv(avol0, buffered(pstate.lnum)), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, buffered(pstate.lnum), lpt2, avol0), bufs-log-only(buffered(pstate.lnum), log1, lpt2), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt2, n0 ' + nx0), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(log1, lpt2), lpt-free-unref(lpt2), lpt-free-unref(lpt0), lpt-leb-size(lpt2), lpt-leb-size(lpt0), lpt-ram-flash(lpt2, lpt0, log1), synced(avol0), istore0 ⊑ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore ⊦ pstate.lnum = n0, pstate = unbuffered, pstate = readonly, dups(log1)

User applied rule constructor cut

And obtained the following new goals

Proof step 132:
# lpt0 = # avol0, # lpt2 = # avol0, lpt2[n0] = mklp(0, m5, LP_FREE, m6), avol0[pstate.lnum] = unmapped, keyset(gch) = gc-heap(lpt2, log1), pstate = journal(n), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, n0 < # avol0, ginval < # avol0, pstate.lnum < # avol0, abs-gstore(avol0, lpt2, gstore, ginval), abs-istore(avol0, lpt2, istore), awbuf-inv(avol0, buffered(pstate.lnum)), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, buffered(pstate.lnum), lpt2, avol0), bufs-log-only(buffered(pstate.lnum), log1, lpt2), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt2, n0 ' + nx0), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt2), lpt-free-unref(lpt0), lpt-free-unref(lpt2), lpt-leb-size(lpt0), lpt-leb-size(lpt2), lpt-ram-flash(lpt2, lpt0, log1), synced(avol0), istore0 ⊑ istore, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore ⊦ pstate.lnum = n0, pstate = readonly, pstate = unbuffered, dups(log1)
Proof step 147:
# lpt0 = # avol0, # lpt2 = # avol0, lpt2[n0] = mklp(0, m5, LP_FREE, m6), avol0[pstate.lnum] = unmapped, keyset(gch) = gc-heap(lpt2, log1), pstate = index(n), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, n0 < # avol0, ginval < # avol0, pstate.lnum < # avol0, abs-gstore(avol0, lpt2, gstore, ginval), abs-istore(avol0, lpt2, istore), awbuf-inv(avol0, buffered(pstate.lnum)), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, buffered(pstate.lnum), lpt2, avol0), bufs-log-only(buffered(pstate.lnum), log1, lpt2), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt2, n0 ' + nx0), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt2), lpt-free-unref(lpt0), lpt-free-unref(lpt2), lpt-leb-size(lpt0), lpt-leb-size(lpt2), lpt-ram-flash(lpt2, lpt0, log1), synced(avol0), istore0 ⊑ istore, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore ⊦ pstate.lnum = n0, pstate = readonly, pstate = unbuffered, dups(log1)

Rule argument

var: pstate

Additional information

Used simplifier rules: persistence-state freely generated by unbuffered, readonly, journal, index ;;