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Proof step 41 from proof inv-truncate (previous step)

gstore2[m] = groupblock(gndx, lax, n1 + m1), dom gstore2 = dom gstore3, remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, as0 ∩ range(fi1 \ datakeys(key, n0, fi1)) = ∅, dom gstore1 ∪ elems nx = dom gstore3 ∪ jro, p_os < pmaxino, fi1.inos < jmaxino, fi2.inos < pmaxino, gstore2 =○refsize gstore3, inv(gstore3 \ jro), inv(gstore1), inv(gstore2 \ jro), inv(gstore2[m, groupblock(gndx, lax, n1)] \ jro), inv(gstore3[nx.last]), refsize-cons(gstore3, range fi1), refsize-cons(gstore1, range fi2), refsize-cons(gstore2, range(fi1 \ datakeys(key, n0, fi1)) ∪ as0), ri-inj(fi1), ri-inj(fi1 \ datakeys(key, n0, fi1)), ri-inj(fi2), valid-journal-head(nx, gstore2, jro), @(m, m0, m1) ∈ as0, m ∈ gstore2, nx.last ∈ gstore3, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore1, as0.lebs ⊆ dom gstore3 ⊦ # as0 = 0, as0 = ∅, nx = [], pmaxino = 0, dups(nx), nx.last ∈ gstore2[m, groupblock(gndx, lax, n1)] ∧ (gstore2[m, groupblock(gndx, lax, n1)][nx.last].gndlist = [] ∨ gstore2[m, groupblock(gndx, lax, n1)][nx.last].gndlist.last.end)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 42:
gstore2[m] = groupblock(gndx, lax, n1 + m1), gstore2[m, groupblock(gndx, lax, n1)][nx.last] = groupblock(gndx0, lax0, m2), dom gstore2 = dom gstore3, remove-refsize0(gstore1) = gstore1, as0 ∩ range(fi1 \ datakeys(key, n0, fi1)) = ∅, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore3 ∪ jro, fi2.inos < pmaxino, fi1.inos < jmaxino, p_os < pmaxino, gstore2 =○refsize gstore3, inv(gstore3[nx.last]), inv(gstore2[m, groupblock(gndx, lax, n1)] \ jro), inv(gstore2 \ jro), inv(gstore1), inv(gstore3 \ jro), refsize-cons(gstore2, range(fi1 \ datakeys(key, n0, fi1)) ∪ as0), refsize-cons(gstore1, range fi2), refsize-cons(gstore3, range fi1), ri-inj(fi2), ri-inj(fi1 \ datakeys(key, n0, fi1)), ri-inj(fi1), valid-journal-head(nx, gstore2, jro), nx.last ∈ gstore3, m ∈ gstore2, @(m, m0, m1) ∈ as0, pmaxino ≤ jmaxino, as0.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore1, fi1.lebs ⊆ dom gstore3 ⊦ # as0 = 0, as0 = ∅, nx = [], pmaxino = 0, dups(nx), nx.last ∈ gstore2[m, groupblock(gndx, lax, n1)] ∧ (gndx0 = [] ∨ gndx0.last.end)

Rule argument

spec: ablock, inst: group-store name: elim seq: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m) subst: [gblock, gndx, lax, m] → [gstore2[m, groupblock(gndx, lax, n1)][nx.last], gndx0, lax0, m2]

Additional information

Used simplifier rules: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m); (elim) Used terms: gstore2[m, groupblock(gndx, lax, n1)][nx.last], gndx0, lax0, m2