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Proof step 23 from proof crash-neutral-set-iblock-refsize (previous step)

istore0[n0] = 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), inv(indexblock(indx, lax, m)), n0 ∈ istore, maxino2 ∈ istore, n0 ∈ istore0, istore0 ⊑ istore, pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2, pstate.index? → pstate.lnum ∈ istore ⊦ m = 0, dups(nx), n0 ∈ remove-refsize0(crash(istore[maxino2, istore[maxino2].ref-size:= n], istore0)) ∧ 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 24:
⊦ n ∈ remove-refsize0(istore) ↔ n ∈ istore ∧ istore[n].ref-size ≠ 0
Proof step 25:
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(indexblock(indx, lax, m)), 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 ⊦ m = 0, dups(nx), ( n0 ∈ crash(istore[maxino2, istore[maxino2].ref-size:= n], istore0) ∧ crash(istore[maxino2, istore[maxino2].ref-size:= n], istore0)[n0].ref-size ≠ 0) ∧ remove-refsize0(crash(istore, istore0))[n0] = remove-refsize0(crash(istore[maxino2, istore[maxino2].ref-size:= n], istore0))[n0]

Rule argument

spec: ablock-store-inv, inst: index-store name: in-remove-refsize0 seq: ⊦ n ∈ remove-refsize0(istore) ↔ n ∈ istore ∧ istore[n].ref-size ≠ 0 subst: [istore, n] → [crash (istore[maxino2, istore[maxino2].ref-size:= n], istore0), n0] flags: <all paths>

Additional information

Used terms: crash(istore[maxino2, istore[maxino2].ref-size:= n], istore0), n0