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Proof step 110 from proof inv-gc (previous step)

# ax = # referenced-adrs(lax.to-adr(n1), fi2), # lax = # gndx0, gstore2[n1].ladrlist = lax, gstore2[n1] = groupblock(gndx0, lax, m0), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓) + ax, nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[ax, nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)]], remove-refsize0(gstore1) = gstore1, elems nx1 ∩ jro0 = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx0 ∩ jro = ∅, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, dom gstore1 ∪ elems nx0 = dom gstore3 ∪ jro, jro1 < jmaxino, p_os < pmaxino, fi2.inos < jmaxino, fi1.inos < pmaxino, fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax].inos < jmaxino0, jro1 < jmaxino0, inv(groupblock(gndx0, lax, m0)), inv(gstore1), inv(gstore2 \ jro0), inv(gstore3 \ jro), new(ax, nodes(gstore2 ↓, jro0)), refsize-cons(gstore2, range fi2), refsize-cons(gstore1, range fi1), refsize-cons(gstore3, (range fi2 \ (range fi2 | n1)) ∪ ax.toSet), ri-cons(fi2, nodes(gstore2 ↓, jro0)), ri-inj(fi2), ri-inj(fi1), ri-inj(fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax]), n1 ∈ gstore3, n1 ∈ dom gstore3 ∪ jro, n1 ∈ gstore1, @(n1, m1, m2) ∈ (range fi2 \ (range fi2 | n1)) ∪ ax.toSet, n1 ∈ gstore2, pmaxino ≤ jmaxino, jmaxino ≤ jmaxino0, pmaxino ≤ jmaxino0, fi2.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, range fi2 ⊆ dom nodes(gstore2 ↓, jro0), dom gstore2 ⊆ dom gstore3, fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax].lebs ⊆ dom gstore3, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3, jro), jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0) ⊦ #((range fi2 \ (range fi2 | n1)) ∪ ax.toSet) = 0, #(dom gstore3 ∪ jro) = 0, jmaxino = 0, jmaxino0 = 0, m0 = 0, pmaxino = 0, dom gstore3 ∪ jro = ∅, (range fi2 \ (range fi2 | n1)) ∪ ax.toSet = ∅, dups(nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys), dups(ax), dups(nx1), dups(nx0), n1 ∈ nx1, n1 ∈ nx0, n1 ∈ jro0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 111:
# ax = # referenced-adrs(gstore2[n1].ladrlist.to-adr(n1), fi2), # gstore2[n1].ladrlist = # gndx0, gstore2[n1] = groupblock(gndx0, gstore2[n1].ladrlist, m0), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓) + ax, nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[ax, nodes(gstore2 ↓, jro0)[referenced-adrs(gstore2[n1].ladrlist.to-adr(n1), fi2)]], remove-refsize0(gstore1) = gstore1, elems nx1 ∩ jro0 = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx0 ∩ jro = ∅, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, dom gstore1 ∪ elems nx0 = dom gstore3 ∪ jro, jro1 < jmaxino, p_os < pmaxino, fi2.inos < jmaxino, fi1.inos < pmaxino, fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(gstore2[n1].ladrlist.to-adr(n1), fi2)].keys, ax].inos < jmaxino0, jro1 < jmaxino0, inv(gstore2[n1]), inv(gstore1), inv(gstore2 \ jro0), inv(gstore3 \ jro), new(ax, nodes(gstore2 ↓, jro0)), refsize-cons(gstore2, range fi2), refsize-cons(gstore1, range fi1), refsize-cons(gstore3, (range fi2 \ (range fi2 | n1)) ∪ ax.toSet), ri-cons(fi2, nodes(gstore2 ↓, jro0)), ri-inj(fi2), ri-inj(fi1), ri-inj(fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(gstore2[n1].ladrlist.to-adr(n1), fi2)].keys, ax]), n1 ∈ gstore3, n1 ∈ dom gstore3 ∪ jro, n1 ∈ gstore1, @(n1, m1, m2) ∈ (range fi2 \ (range fi2 | n1)) ∪ ax.toSet, n1 ∈ gstore2, pmaxino ≤ jmaxino, jmaxino ≤ jmaxino0, pmaxino ≤ jmaxino0, fi2.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, range fi2 ⊆ dom nodes(gstore2 ↓, jro0), dom gstore2 ⊆ dom gstore3, fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(gstore2[n1].ladrlist.to-adr(n1), fi2)].keys, ax].lebs ⊆ dom gstore3, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3, jro), jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0) ⊦ #((range fi2 \ (range fi2 | n1)) ∪ ax.toSet) = 0, #(dom gstore3 ∪ jro) = 0, jmaxino = 0, jmaxino0 = 0, m0 = 0, pmaxino = 0, dom gstore3 ∪ jro = ∅, (range fi2 \ (range fi2 | n1)) ∪ ax.toSet = ∅, dups(nodes(gstore2 ↓, jro0)[referenced-adrs(gstore2[n1].ladrlist.to-adr(n1), fi2)].keys), dups(ax), dups(nx1), dups(nx0), n1 ∈ nx1, n1 ∈ nx0, n1 ∈ jro0

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ as ≠ ∅ → # as ≠ 0; (forward) from specification set-basic[node-store]%ne-01: ⊦ adr ∈ as → as ≠ ∅; (forward) from specification set-basic[node-store]%fwd-inv-gblock-rem: ⊦ inv(gstore \ ginval) ∧ n ∈ gstore ∧ ¬ n ∈ ginval ∧ gstore[n] = gblock → inv(gblock); (forward) from specification apersistence-base