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Proof step 36 from proof inv-deallocate-gnd (previous step)

# lpt0 = # avol, # lpt2 = # avol, lpt2[n] = mklp(m3, m1, LP_GROUP_NODES, m2), keyset(gch0) = gc-heap(lpt2, log0) -- key-index(m3, n), keyset(gch) = gc-heap(lpt2, log0), n < # avol, awbuf-inv(avol, bleb), bin-heap-inv(gch0, lpt), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, bleb, lpt2, avol), bufs-log-only(bleb, log0, lpt2), freelist-cons(lpt2, freelist), id-idx(lpt2[n, mklp(0, 0, LP_FREE, m2)], lpt), log-group-block(log0, lpt2), lpt-free-unref(lpt0), lpt-free-unref(lpt2), lpt-leb-size(lpt0), lpt-leb-size(lpt2), lpt-ram-flash(lpt2, lpt0, log0), synced(avol), key-index(m3, n) ∈ gc-heap(lpt2, log0) ⊦ # gc-heap(lpt2, log0) = 0, buffered(n) = bleb, gc-heap(lpt2, log0) = ∅, dups(log0), n ∈ log0, bufs-log-only(bleb, log0, lpt2[n, mklp(0, 0, LP_FREE, m2)]) ∧ # lpt = # avol ∧ log-group-block(log0, lpt) ∧ lpt-ram-flash(lpt, lpt0, log0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ id-idx(lpt0, lpt1) ∧ log-group-block(nx, lpt0) → log-group-block(nx, lpt1)
Proof step 38:
# lpt2 = # avol, # lpt0 = # avol, lpt2[n] = mklp(m3, m1, LP_GROUP_NODES, m2), keyset(gch) = gc-heap(lpt2, log0), keyset(gch0) = gc-heap(lpt2, log0) -- key-index(m3, n), n < # avol, awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt2), bin-heap-inv(gch0, lpt), buf-ro-rw-mode(false, bleb, lpt2, avol), bufs-log-only(bleb, log0, lpt2), freelist-cons(lpt2, freelist), id-idx(lpt2[n, mklp(0, 0, LP_FREE, m2)], lpt), log-group-block(log0, lpt2), lpt-free-unref(lpt2), lpt-free-unref(lpt0), lpt-leb-size(lpt2), lpt-leb-size(lpt0), lpt-ram-flash(lpt2, lpt0, log0), synced(avol), key-index(m3, n) ∈ gc-heap(lpt2, log0) ⊦ # gc-heap(lpt2, log0) = 0, buffered(n) = bleb, gc-heap(lpt2, log0) = ∅, dups(log0), n ∈ log0, bufs-log-only(bleb, log0, lpt2[n, mklp(0, 0, LP_FREE, m2)]) ∧ # lpt = # avol ∧ log-group-block(log0, lpt) ∧ lpt-ram-flash(lpt, lpt0, log0), id-idx(lpt2[n, mklp(0, 0, LP_FREE, m2)], lpt) ∧ log-group-block(log0, lpt2[n, mklp(0, 0, LP_FREE, m2)])
Proof step 47:
# lpt2 = # avol, # lpt0 = # avol, lpt2[n] = mklp(m3, m1, LP_GROUP_NODES, m2), keyset(gch) = gc-heap(lpt2, log0), keyset(gch0) = gc-heap(lpt2, log0) -- key-index(m3, n), n < # avol, awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt2), bin-heap-inv(gch0, lpt), buf-ro-rw-mode(false, bleb, lpt2, avol), bufs-log-only(bleb, log0, lpt2), freelist-cons(lpt2, freelist), id-idx(lpt2[n, mklp(0, 0, LP_FREE, m2)], lpt), log-group-block(log0, lpt2), log-group-block(log0, lpt2[n, mklp(0, 0, LP_FREE, m2)]), lpt-free-unref(lpt2), lpt-free-unref(lpt0), lpt-leb-size(lpt2), lpt-leb-size(lpt0), lpt-ram-flash(lpt2, lpt0, log0), synced(avol), key-index(m3, n) ∈ gc-heap(lpt2, log0) ⊦ # gc-heap(lpt2, log0) = 0, buffered(n) = bleb, gc-heap(lpt2, log0) = ∅, dups(log0), n ∈ log0, bufs-log-only(bleb, log0, lpt2[n, mklp(0, 0, LP_FREE, m2)]) ∧ # lpt = # avol ∧ true ∧ lpt-ram-flash(lpt, lpt0, log0)

Rule argument

spec: persistence-base name: log-group-block-id-idx seq: ⊦ id-idx(lpt0, lpt1) ∧ log-group-block(nx, lpt0) → log-group-block(nx, lpt1) subst: [lpt0, lpt1, nx] → [lpt2[n, mklp(0, 0, LP_FREE, m2)], lpt, log0] flags: <all paths>

Additional information

Used terms: lpt2[n, mklp(0, 0, LP_FREE, m2)], lpt, log0