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Proof step 16 from proof crash-neutral-set-iblock-refsize (previous step)

crash(istore, istore0)[n0] = indexblock(indx, lax, m), remove-refsize0(istore0) = istore0, remove-refsize0(gstore1) = gstore1, elems nx ∩ ginval1 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval1, inv(istore0), inv(istore), inv(gstore1), inv(gstore2 \ ginval1), n0 ∈ istore0, maxino2 ∈ istore, n0 ∈ istore, istore0 ⊑ istore, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2 ⊦ dups(nx), (m ≠ 0 ↔ n0 ∈ remove-refsize0(crash(istore[maxino2, istore[maxino2].ref-size:= n], istore0))) ∧ (m ≠ 0 → remove-refsize0(crash(istore, istore0))[n0] = remove-refsize0(crash(istore[maxino2, istore[maxino2].ref-size:= n], istore0))[n0])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ n ∈ istore0 → crash(istore, istore0)[n] = indexblock(istore[n].indlist, istore[n].ladrlist, istore0[n].ref-size)
Proof step 18:
indexblock(istore[n0].indlist, istore[n0].ladrlist, istore0[n0].ref-size) = indexblock(indx, lax, m), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore0) = istore0, elems nx ∩ ginval1 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval1, inv(gstore2 \ ginval1), inv(gstore1), inv(istore), inv(istore0), n0 ∈ istore, maxino2 ∈ istore, n0 ∈ istore0, istore0 ⊑ istore, pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2, pstate.index? → pstate.lnum ∈ istore ⊦ dups(nx), (m ≠ 0 ↔ n0 ∈ remove-refsize0(crash(istore[maxino2, istore[maxino2].ref-size:= n], istore0))) ∧ (m ≠ 0 → remove-refsize0(crash(istore, istore0))[n0] = remove-refsize0(crash(istore[maxino2, istore[maxino2].ref-size:= n], istore0))[n0])

Rule argument

spec: apersistence-base name: crash-index-at seq: ⊦ n ∈ istore0 → crash(istore, istore0)[n] = indexblock (istore[n].indlist, istore[n].ladrlist, istore0[n].ref-size) subst: [n, istore0, istore] → [n0, istore0, istore] flags: <all paths>

Additional information

Used terms: n0, istore0, istore