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Proof step 139 from proof refine-allocate-ind (previous step)

# lpt0 = # avol0, # lpt2 = # avol0, avol0[log1.last] = unmapped, lpt2[n0] = mklp(0, m5, LP_FREE, m6), gstore[log1.last] = groupblock(gndx, lax, m), lpt2[log1.last] = mklp(m, m0, LP_GROUP_NODES, m1), keyset(gch) = gc-heap(lpt2, log1), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, log1.last < # avol0, n0 < # avol0, ginval < # 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(groupblock(gndx, lax, m)), 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), log1.last ∈ gstore, istore0 ⊑ istore ⊦ log1.last = n0, dups(log1), ∀ nx0, n. log1 ≠ nx0 + n '

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 140:
# lpt2 = # avol0, # lpt0 = # avol0, (elems nx ∪ dom gstore0) ++ n = dom gstore ∪ ginval, lpt2[n] = mklp(m, m0, LP_GROUP_NODES, m1), gstore[n] = groupblock(gndx, lax, m), lpt2[n0] = mklp(0, m5, LP_FREE, m6), avol0[n] = unmapped, keyset(gch) = gc-heap(lpt2, nx + n '), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, ginval ∩ elems nx = ∅, ginval < # avol0, n0 < # avol0, n < # avol0, abs-gstore(avol0, lpt2, gstore, ginval), abs-istore(avol0, lpt2, istore), awbuf-inv(avol0, buffered(n)), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, buffered(n), lpt2, avol0), bufs-log-only(buffered(n), nx + n ', lpt2), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt2, n0 ' + nx0), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), inv(groupblock(gndx, lax, m)), log-group-block(nx + n ', lpt2), lpt-free-unref(lpt2), lpt-free-unref(lpt0), lpt-leb-size(lpt2), lpt-leb-size(lpt0), lpt-ram-flash(lpt2, lpt0, nx + n '), synced(avol0), n ∈ gstore, istore0 ⊑ istore ⊦ n = n0, dups(nx), n ∈ ginval, n ∈ nx

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;% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)% ⊦ groupblock(gndx, lax, m).ref-size = m; (s)% ⊦ mklp(n2, n3, lpf, m).ref-size = n2; (s)%fwd-inv-gblock-rem: ⊦ inv(gstore \ ginval) ∧ n ∈ gstore ∧ ¬ n ∈ ginval ∧ gstore[n] = gblock → inv(gblock); (forward) from specification apersistence-base%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% ⊦ dups(nx + n ') ↔ n ∈ nx ∨ dups(nx); (ws)% ⊦ (nx + n ').last = n; (s)%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]% ⊦ ns ∩ (ns0 ++ n) = ∅ ↔ ns ∩ ns0 = ∅ ∧ ¬ n ∈ ns; (ws)%unc: ⊦ ns ∪ ns0 = ns0 ∪ ns; from specification set-union[nat-set]%una: ⊦ (ns ∪ ns0) ∪ ns1 = ns ∪ ns0 ∪ ns1; from specification set-union[nat-set]% ⊦ (ns ++ n) ∪ ns0 = (ns ∪ ns0) ++ n; (s)%a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]% ⊦ elems(nx0 + n ') = elems nx0 ++ n; (s)