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Proof step 59 from proof crash-neutral-set-iblock-refsize (previous step)

istore[n0] = indexblock(indx0, lax0, m0), istore[maxino2, istore[maxino2].ref-size:= n][n0] = indexblock(indx1, lax1, m1), 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), inv(indexblock(indx0, lax0, m0)), maxino2 ∈ istore, n0 ∈ istore, n0 ∈ istore0, istore0 ⊑ istore, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2 ⊦ indexblock(indx0, lax0, m) = indexblock(indx1, lax1, m), m = 0, dups(nx)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store, inst: index-store-ablock-store-nat-store name: At-other seq: ⊦ n ≠ n0 → istore[n0, iblock][n] = istore[n] subst: [n, iblock, n0, istore] → [n0, istore[maxino2].ref-size:= n, maxino2, istore] flags: <all paths>

Additional information

Used simplifier rules: ⊦ indexblock(indx, lax, m) = indexblock(indx0, lax0, m0) ↔ indx = indx0 ∧ lax = lax0 ∧ m = m0; (ws)% ⊦ istore[n, iblock][n] = iblock; (s)%prefix-fwd-in: ⊦ istore ⊑ istore0 ∧ n ∈ istore → n ∈ istore0; (forward) from specification ablock-store-inv[index-store]% ⊦ indexblock(indx, lax, m).ref-size:= m0 = indexblock(indx, lax, m0); (s) Used terms: n0, istore[maxino2].ref-size:= n, maxino2, istore