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Proof step 25 from proof recovery (previous step)

# lpt2 = # avol0, # lpt4 = # avol0, keyset(gch1) = gc-heap(lpt2, log3), remove-refsize0(istore2) = istore2, remove-refsize0(gstore2) = gstore2, elems log3 ∩ ns3 = ∅, dom gstore2 ∪ elems log3 = dom gstore1 ∪ ns3, ns3 < # avol0, abs-gstore(avol0, lpt2, gstore1, ns3), abs-istore(avol0, lpt2, istore1), awbuf-inv(avol0, bleb1), bin-heap-inv(gch1, lpt2), buf-ro-rw-mode(pstate0 = readonly, bleb1, lpt2, avol0), bufs-log-only(bleb1, log3, lpt2), flash-lpt-cons(lpt4, istore2, gstore2), freelist-cons(lpt2, log4), inv(istore2), inv(istore1), inv(gstore2), inv(gstore1 \ ns3), log-group-block(log3, lpt2), lpt-free-unref(lpt2), lpt-free-unref(lpt4), lpt-leb-size(lpt2), lpt-leb-size(lpt4), lpt-ram-flash(lpt2, lpt4, log3), synced(avol0), avol ↓ avol0, istore2 ⊑ istore1, pstate0 = unbuffered → isbuf0, pstate0.index? → pstate0.lnum ∈ istore1, pstate0.journal? → log3 ≠ [] ∧ pstate0.lnum = log3.last ∧ pstate0.lnum ∈ gstore1, pstate0 ≠ unbuffered ∧ pstate0 ≠ readonly → bleb1 = buffered(pstate0.lnum), pstate0 = unbuffered → bleb1 = nobuffer ⊦ dups(log3), valid-indices(lpt4, log3)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array-indices, inst: lp-array name: valid-indices-nonrec seq: ⊦ valid-indices(lpt, nx) ↔ (∀ n. n ∈ nx → n < # lpt) subst: [nx, lpt] → [log3, lpt4] flags: <all paths>

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;% ⊦ m < n ↔ ¬ n ≤ m; (ss)%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]%int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set]%elems-in-notin-ginval: ⊦ n ∈ nx ∧ elems nx ∩ ns = ∅ → ¬ n ∈ ns; (forward) from specification apersistence-base%una: ⊦ (ns ∪ ns0) ∪ ns1 = ns ∪ ns0 ∪ ns1; from specification set-union[nat-set]%unc: ⊦ ns ∪ ns0 = ns0 ∪ ns; from specification set-union[nat-set]%fwd-in-log-in-gstore: ⊦ n ∈ nx ∧ ginval ∩ elems nx = ∅ ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval → n ∈ gstore; (forward) from specification apersistence-base% ⊦ unbuffered ≠ readonly; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)%⊦ ¬ pstate.journal? → (pstate.index? ↔ pstate ≠ unbuffered ∧ pstate ≠ readonly); (ss)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ ¬ natkey < natkey; (s) Used terms: log3, lpt4