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Proof step 40 from proof inv-remove (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 41:
fi2[key] = @(m, m0, m1), gstore2[m] = groupblock(gndx, lax, n0 + m1), gstore2[m, groupblock(gndx, lax, n0)][nx.last] = groupblock(gndx0, lax0, m2), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro, p_os < pmaxino, fi2.inos < jmaxino, fi1.inos < pmaxino, inv(gstore2[nx.last]), inv(gstore2[m, groupblock(gndx, lax, n0)] \ jro), inv(gstore2 \ jro), inv(gstore1), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range fi2), ri-inj(fi1), ri-inj(fi2 -- key), ri-inj(fi2), valid-journal-head(nx, gstore2, jro), nx.last ∈ gstore2[m, groupblock(gndx, lax, n0)], nx.last ∈ gstore2, key ∈ fi2, m ∈ gstore2, pmaxino ≤ jmaxino, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1 ⊦ gndx0 = [], nx = [], pmaxino = 0, gndx0.last.end, dups(nx)

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, n0)][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, n0)][nx.last], gndx0, lax0, m2