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Proof step 135 from proof refine-allocate-ind (previous step)

# lpt2 = # avol0, # lpt0 = # avol0, lpt2[log1.last].flags = LP_GROUP_NODES, gstore[log1.last] = groupblock(gndx, lax, lpt2[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(groupblock(gndx, lax, lpt2[log1.last].ref-size)), 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)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 136:
# 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, lpf, m1), keyset(gch) = gc-heap(lpt2, log1), lpf = LP_GROUP_NODES, 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, log1 = [], dups(log1)

Rule argument

spec: lprops name: elim seq: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1) subst: [lp, m, m0, lpf, m1] → [lpt2[log1.last], m, m0, lpf, m1]

Additional information

Used simplifier rules: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1); (elim) Used terms: lpt2[log1.last], m, m0, lpf, m1