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Proof step 132 from proof refine-allocate-ind (previous step)

# 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 133:
# lpt2 = # avol0, # lpt0 = # avol0, lpt2[log1.last].flags = LP_GROUP_NODES, lpt2[log1.last].ref-size = gstore[log1.last].ref-size, lpt2[n0] = mklp(0, m5, LP_FREE, m6), avol0[log1.last] = unmapped, keyset(gch) = gc-heap(lpt2, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol0, n0 < # avol0, log1.last < # avol0, abs-gstore(avol0, lpt2, gstore, ginval), abs-istore(avol0, lpt2, istore), awbuf-inv(avol0, buffered(log1.last)), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, buffered(log1.last), lpt2, avol0), bufs-log-only(buffered(log1.last), log1, lpt2), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt2, n0 ' + nx0), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), inv(gstore[log1.last]), 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), log1.last ∈ gstore, istore0 ⊑ istore ⊦ log1.last = n0, log1 = [], dups(log1)

Rule argument

Additional information

Used simplifier rules: fwd-in-gstore-lpt: ⊦ n ∈ gstore ∧ abs-gstore(avol, lpt, gstore, ginval) → n < # lpt ∧ lpt[n].ref-size = gstore[n].ref-size ∧ lpt[n].flags = LP_GROUP_NODES;%fwd-inv-loghead: ⊦ nx ≠ [] ∧ inv(gstore \ ginval) ∧ ginval ∩ elems nx = ∅ ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval → inv(gstore[nx.last]); (forward) from specification apersistence-base%fwd-in-gstore-loghead: ⊦ nx ≠ [] ∧ ginval ∩ elems nx = ∅ ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval → nx.last ∈ gstore; (forward) from specification apersistence-base%unc: ⊦ ns ∪ ns0 = ns0 ∪ ns; from specification set-union[nat-set]%una: ⊦ (ns ∪ ns0) ∪ ns1 = ns ∪ ns0 ∪ ns1; from specification set-union[nat-set]%int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set]%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]%inv-buf-in-vol: ⊦ awbuf-inv(avol, buffered(n)) → n < # avol; (forward) from specification awbuf-inv%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ ¬ journal(m).index?; (s)% ⊦ journal(m).journal?; (s)% ⊦ readonly ≠ journal(m); (s)% ⊦ unbuffered ≠ journal(m); (s)% ⊦ journal(m).lnum = m; (s)