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Proof step 112 from proof refine-allocate-gnd (previous step)

# lpt0 = # avol0, # lpt = # avol0, lpt[n0] = mklp(0, m1, LP_FREE, m4), keyset(gch) = gc-heap(lpt, log1), remove-refsize0(istore1) = istore1, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, n0 < # avol0, ginval < # avol0, abs-gstore(avol0, lpt, gstore, ginval), abs-istore(avol0, lpt, istore2), awbuf-inv(avol0, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(false, bleb, lpt, avol0), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt, n0 ' + nx0), inv(istore1), inv(istore2), 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), synced(avol0), istore1 ⊑ istore2, pstate ≠ unbuffered → bleb = buffered(pstate.lnum), pstate.index? → pstate.lnum ∈ istore2, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate = unbuffered → bleb = nobuffer ⊦ pstate = readonly, dups(log1), abs-gstore (avol0[journal(n0).lnum, mapped(mkbuf(0))], lpt[journal(n0).lnum, mklp(0, 0, LP_GROUP_NODES, m4)], gstore[n0, groupblock([], [], 0)], ginval -- n0) ∧ log1 + n0 ' = log1 + journal(n0).lnum ' ∧ ginval -- n0 < # avol0 ∧ journal(n0) ≠ unbuffered ∧ journal(n0) ≠ readonly ∧ n0 = journal(n0).lnum

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 113:
# lpt = # avol0, # lpt0 = # avol0, lpt[n0] = mklp(0, m1, LP_FREE, m4), keyset(gch) = gc-heap(lpt, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore1) = istore1, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol0, n0 < # avol0, abs-gstore(avol0, lpt, gstore, ginval), abs-istore(avol0, lpt, istore2), awbuf-inv(avol0, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(false, bleb, lpt, avol0), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt, n0 ' + nx0), inv(gstore \ ginval), inv(gstore0), inv(istore2), inv(istore1), 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), synced(avol0), istore1 ⊑ istore2, pstate = unbuffered → bleb = nobuffer, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore2, pstate ≠ unbuffered → bleb = buffered(pstate.lnum) ⊦ pstate = readonly, abs-gstore(avol0[n0, mapped(mkbuf(0))], lpt[n0, mklp(0, 0, LP_GROUP_NODES, m4)], gstore[n0, groupblock([], [], 0)], ginval -- n0), dups(log1)

Rule argument

Additional information

Used simplifier rules: ⊦ readonly ≠ journal(m); (s)% ⊦ unbuffered ≠ journal(m); (s)% ⊦ ns < n → ns -- n0 < n; (s)%a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]% ⊦ nx + nx0 = nx + nx1 ↔ nx0 = nx1; (s)% ⊦ journal(m).lnum = m; (s)