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Proof step 74 from proof refine-deallocate-gnd (previous step)

# lpt2 = # avol, # lpt0 = # avol, lpt2[n] = mklp(m3, m1, LP_GROUP_NODES, m2), gstore[n] = groupblock(gndx, lax, m3), keyset(gch0) = gc-heap(lpt2, log1) -- key-index(m3, n), keyset(gch) = gc-heap(lpt2, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore1) = istore1, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, n < # avol, ginval < # avol, abs-gstore(avol, lpt2, gstore, ginval), abs-istore(avol, lpt2, istore2), 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, log1, lpt2), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt2, freelist), id-idx(lpt2[n, mklp(0, 0, LP_FREE, m2)], lpt), inv(gstore \ ginval), inv(gstore0), inv(istore2), inv(istore1), 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(avol), n ∈ gstore, n ∈ gstore0, key-index(m3, n) ∈ gc-heap(lpt2, log1), istore1 ⊑ istore2, pstate ≠ unbuffered → bleb = buffered(pstate.lnum), pstate = unbuffered → bleb = nobuffer, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore2 ⊦ # gc-heap(lpt2, log1) = 0, buffered(n) = bleb, gc-heap(lpt2, log1) = ∅, pstate = readonly, ginval ++ n < # lpt, dups(log1), n ∈ log1

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% ⊦ ns < n → (ns ++ n0 < n ↔ n0 < n); (ss)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s) Used terms: lpt, lpt2[n, mklp(0, 0, LP_FREE, m2)]