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Proof step 57 from proof inv-deallocate-gnd (previous step)

# 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, # lpt = # avol, buffered(n) = bleb, gc-heap(lpt2, log0) = ∅, dups(log0), n ∈ log0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: index-array, inst: gc-heap-base name: id-idx seq: ⊦ id-idx(lpt1, lpt0) ↔ # lpt0 = # lpt1 ∧ (∀ n. n < # lpt0 → lpt1[n].ref-size = lpt0[n].ref-size ∧ lpt1[n].size = lpt0[n].size ∧ lpt1[n].flags = lpt0[n].flags) subst: [lpt0, lpt1] → [lpt, lpt2[n, mklp(0, 0, LP_FREE, m2)]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # lpt[n, lp] = # lpt; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic Used terms: lpt, lpt2[n, mklp(0, 0, LP_FREE, m2)]