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Proof step 12 from proof inv-set-iblock-refsize (previous step)

istore0[n0] = indexblock(indx, lax, m), istore[maxino2, istore[maxino2].ref-size:= n][n0] = indexblock(indx0, lax0, m0), remove-refsize0(istore0) = istore0, remove-refsize0(gstore1) = gstore1, elems nx ∩ ginval2 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval2, inv(istore0), inv(istore), inv(gstore1), inv(gstore2 \ ginval2), inv(istore[maxino2, istore[maxino2].ref-size:= n]), maxino2 ∈ istore, istore0 ⊑ istore, pstate = unbuffered → syn, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2 ⊦ dups(nx), (pstate.index? → pstate.lnum ∈ istore[maxino2, istore[maxino2].ref-size:= n]) ∧ (n0 ∈ istore0 ∧ n0 ∈ istore[maxino2, istore[maxino2].ref-size:= n] → indx ⊑ indx0 ∧ lax ⊑ lax0 ∧ # indx = # lax ∧ # indx0 = # lax0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ istore ⊑ istore0 ↔ dom istore ⊆ dom istore0 ∧ (∀ n. n ∈ istore ∧ n ∈ istore0 → istore[n].indlist ⊑ istore0[n].indlist ∧ istore[n].ladrlist ⊑ istore0[n].ladrlist ∧ # istore[n].indlist = # istore[n].ladrlist ∧ # istore0[n].indlist = # istore0[n].ladrlist)
Proof step 14:
istore[maxino2, istore[maxino2].ref-size:= n][n0] = indexblock(indx0, lax0, m0), istore0[n0] = indexblock(indx, lax, m), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore0) = istore0, elems nx ∩ ginval2 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval2, inv(istore[maxino2, istore[maxino2].ref-size:= n]), inv(gstore2 \ ginval2), inv(gstore1), inv(istore), inv(istore0), maxino2 ∈ istore, dom istore0 ⊆ dom istore, pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2, pstate.index? → pstate.lnum ∈ istore, pstate = unbuffered → syn, ∀ n. n ∈ istore0 ∧ n ∈ istore → istore0[n].indlist ⊑ istore[n].indlist ∧ istore0[n].ladrlist ⊑ istore[n].ladrlist ∧ # istore0[n].indlist = # istore0[n].ladrlist ∧ # istore[n].indlist = # istore[n].ladrlist ⊦ dups(nx), (pstate.index? → pstate.lnum ∈ istore[maxino2, istore[maxino2].ref-size:= n]) ∧ (n0 ∈ istore0 ∧ n0 ∈ istore[maxino2, istore[maxino2].ref-size:= n] → indx ⊑ indx0 ∧ lax ⊑ lax0 ∧ # indx = # lax ∧ # indx0 = # lax0)

Rule argument

spec: ablock-store-inv, inst: index-store name: blockstore-prefix seq: ⊦ istore ⊑ istore0 ↔ dom istore ⊆ dom istore0 ∧ (∀ n. n ∈ istore ∧ n ∈ istore0 → istore[n].indlist ⊑ istore0[n].indlist ∧ istore[n].ladrlist ⊑ istore0[n].ladrlist ∧ # istore[n].indlist = # istore[n].ladrlist ∧ # istore0[n].indlist = # istore0[n].ladrlist) subst: [istore0, istore] → [istore, istore0] flags: <all paths>

Additional information

Used terms: istore, istore0