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Proof step 138 from proof inv-store (previous step)

gstore3[m0] = groupblock(gndx, lax, m3), gstore3[@(m0, m1, m2)] = mkgnode(nd, m, boolvar, boolvar0), jvalid1, remove-refsize0(gstore2) = gstore2, elems nx ∩ jro0 = ∅, dom gstore2 ∪ elems nx = dom gstore3 ∪ jro0, fi1.inos < pmaxino, fi2.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, inv(gstore2), inv(gstore3 \ jro0), inv(gstore3[m0, groupblock(gndx, lax, m3 + m2)] \ jro0), key-cons(key, nd), refsize-cons(gstore2, range fi1), refsize-cons(gstore3, range fi2), ri-inj(fi1), ri-inj(fi2[key, @(m0, m1, m2)]), ri-inj(fi2), @(m0, m1, m2) ∈ gstore3, m0 ∈ gstore3, pmaxino ≤ jmaxino, pmaxino ≤ max(key.ino + 1, jmaxino), fi1.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore3, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro0) ⊦ jmaxino = 0, max(key.ino + 1, jmaxino) = 0, nx = [], pmaxino = 0, dups(nx), valid-journal-head(nx, gstore3[m0, groupblock(gndx, lax, m3 + m2)], jro0), key ∈ fi2, @(m0, m1, m2) ∈ fi2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 139:
gstore3[@(m0, m1, m2)] = mkgnode(nd, m, boolvar, boolvar0), gstore3[m0] = groupblock(gndx, lax, m3), remove-refsize0(gstore2) = gstore2, elems nx ∩ jro0 = ∅, dom gstore2 ∪ elems nx = dom gstore3 ∪ jro0, jro1 < jmaxino, p_os < pmaxino, fi2.inos < jmaxino, fi1.inos < pmaxino, inv(gstore3[m0, groupblock(gndx, lax, m3 + m2)] \ jro0), inv(gstore3 \ jro0), inv(gstore2), inv(gstore3[nx.last]), key-cons(key, nd), refsize-cons(gstore3, range fi2), refsize-cons(gstore2, range fi1), ri-inj(fi2), ri-inj(fi2[key, @(m0, m1, m2)]), ri-inj(fi1), valid-journal-head(nx, gstore3, jro0), m0 ∈ gstore3, @(m0, m1, m2) ∈ gstore3, nx.last ∈ gstore3, pmaxino ≤ max(key.ino + 1, jmaxino), pmaxino ≤ jmaxino, fi2.lebs ⊆ dom gstore3, fi1.lebs ⊆ dom gstore2 ⊦ jmaxino = 0, max(key.ino + 1, jmaxino) = 0, nx = [], pmaxino = 0, dups(nx), valid-journal-head(nx, gstore3[m0, groupblock(gndx, lax, m3 + m2)], jro0), @(m0, m1, m2) ∈ fi2, key ∈ fi2

Rule argument

Additional information

Used simplifier rules: fwd-inv-loghead: ⊦ nx ≠ [] ∧ inv(gstore \ ginval) ∧ ginval ∩ elems nx = ∅ ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval → inv(gstore[nx.last]); (forward) from specification apersistence-base%fwd-in-gstore-loghead: ⊦ nx ≠ [] ∧ ginval ∩ elems nx = ∅ ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval → nx.last ∈ gstore; (forward) from specification apersistence-base%unc: ⊦ ns ∪ ns0 = ns0 ∪ ns; from specification set-union[nat-set]%una: ⊦ (ns ∪ ns0) ∪ ns1 = ns ∪ ns0 ∪ ns1; from specification set-union[nat-set]%int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set]%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]