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Proof step 48 from proof crash-neutral-set-iblock-refsize (previous step)

crash(istore, istore0)[n0] = indexblock(indx0, lax0, m0), 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 ⊦ crash(istore[maxino2, istore[maxino2].ref-size:= n], istore0)[n0].ref-size = 0, indexblock(indx0, lax0, m0) = crash(istore[maxino2, istore[maxino2].ref-size:= n], istore0)[n0], m = 0, m0 = 0, dups(nx)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 49:
istore0[n0] = indexblock(indx, lax, m), crash(istore, istore0)[n0] = indexblock(indx0, lax0, m0), crash(istore[maxino2, istore[maxino2].ref-size:= n], istore0)[n0] = indexblock(indx1, lax1, m1), 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 ⊦ indexblock(indx0, lax0, m0) = crash(istore[maxino2, istore[maxino2].ref-size:= n], istore0)[n0], m = 0, m0 = 0, m1 = 0, dups(nx)

Rule argument

spec: ablock, inst: index-store name: elim seq: ⊦ (indx = iblock.indlist ∧ lax = iblock.ladrlist) ∧ m = iblock.ref-size ↔ iblock = indexblock(indx, lax, m) subst: [iblock, indx, lax, m] → [crash (istore[maxino2, istore[maxino2].ref-size:= n], istore0) [n0 ], indx1, lax1, m1]

Additional information

Used simplifier rules: ⊦ (indx = iblock.indlist ∧ lax = iblock.ladrlist) ∧ m = iblock.ref-size ↔ iblock = indexblock(indx, lax, m); (elim) Used terms: crash(istore[maxino2, istore[maxino2].ref-size:= n], istore0)[n0], indx1, lax1, m1