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Proof step 78 from proof refine-deallocate-gnd (previous step)

# lpt0 = # avol, # lpt1 = # avol, gstore[pstate.lnum] = groupblock(gndx, lax, m3), lpt1[pstate.lnum] = mklp(m3, m1, LP_GROUP_NODES, m2), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, pstate.lnum < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), awbuf-inv(avol, buffered(pstate.lnum)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(pstate.lnum), lpt1, avol), bufs-log-only(buffered(pstate.lnum), log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, log1), synced(avol), pstate.lnum ∈ gstore, pstate.lnum ∈ gstore0, istore0 ⊑ istore, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ⊦ pstate = unbuffered, pstate = readonly, dups(log1), pstate.lnum ∈ log1

User applied rule constructor cut

And closed the goal!

Rule argument

var: pstate

Additional information

Used simplifier rules: fwd-in-istore-lpt: ⊦ n ∈ istore ∧ abs-istore(avol, lpt, istore) → n < # lpt ∧ lpt[n].ref-size = istore[n].ref-size ∧ lpt[n].flags = LP_INDEX_NODES;%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;%persistence-state freely generated by unbuffered, readonly, journal, index ;;% ⊦ index(m).lnum = m; (s)% ⊦ unbuffered ≠ index(m); (s)% ⊦ readonly ≠ index(m); (s)% ⊦ index(m).index?; (s)% ⊦ ¬ index(m).journal?; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%inv-buf-in-vol: ⊦ awbuf-inv(avol, buffered(n)) → n < # avol; (forward) from specification awbuf-inv%una: ⊦ (ns ∪ ns0) ∪ ns1 = ns ∪ ns0 ∪ ns1; from specification set-union[nat-set]%unc: ⊦ ns ∪ ns0 = ns0 ∪ ns; from specification set-union[nat-set]%fwd-in-gstore0: ⊦ n ∈ gstore ∧ ¬ n ∈ nx ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval → n ∈ gstore0; (forward) from specification apersistence-base% ⊦ mklp(n2, n3, lpf, m).ref-size = n2; (s)% ⊦ groupblock(gndx, lax, m).ref-size = m; (s)% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)% ⊦ LP_GROUP_NODES ≠ LP_INDEX_NODES; (s)% ⊦ journal(m).lnum = m; (s)% ⊦ unbuffered ≠ journal(m); (s)% ⊦ readonly ≠ journal(m); (s)% ⊦ ¬ journal(m).index?; (s)% ⊦ journal(m).journal?; (s)% ⊦ nx.last = n ∧ nx ≠ [] → n ∈ nx; (s)