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Proof step 43 from proof inv-remove (previous step)

gndx0.last = mkgnode(nd, m3, boolvar, false), 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, dups(nx)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 44:
⊦ valid-journal-head(nx, gstore, ginval) ↔ nx ≠ [] ∧ nx.last ∈ gstore ∧ ¬ nx.last ∈ ginval ∧ (gstore[nx.last].gndlist = [] ∨ gstore[nx.last].gndlist.last.end)
Proof step 45:
gndx0.last = mkgnode(nd, m3, boolvar, false), gstore2[m, groupblock(gndx, lax, n0)][nx.last] = groupblock(gndx0, lax0, m2), 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), m ∈ gstore2, key ∈ fi2, nx.last ∈ gstore2[m, groupblock(gndx, lax, n0)], nx.last ∈ gstore2, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, fi2.lebs ⊆ dom gstore2, gstore2[nx.last].gndlist = [] ∨ gstore2[nx.last].gndlist.last.end ⊦ gndx0 = [], nx = [], pmaxino = 0, dups(nx), nx.last ∈ jro

Rule argument

spec: gjournal-base name: valid-journal-head seq: ⊦ valid-journal-head(nx, gstore, ginval) ↔ nx ≠ [] ∧ nx.last ∈ gstore ∧ ¬ nx.last ∈ ginval ∧ ( gstore[nx.last].gndlist = [] ∨ gstore[nx.last].gndlist.last.end) subst: [ginval, gstore, nx] → [jro, gstore2, nx] flags: <all paths>

Additional information

Used terms: jro, gstore2, nx