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Proof step 212 from proof refine-gc (previous step)

# lax = # gndx0, # ax0 = # referenced-adrs(lax.to-adr(n1), ri0), gstore2[n1].ladrlist = lax, gstore2[n1] = groupblock(gndx0, lax, m0), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓) + ax0, nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[ax0, nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri0)]], remove-refsize0(gstore1) = gstore1, elems nx1 ∩ jro0 = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx0 ∩ jro = ∅, dom gstore1 ∪ elems nx0 = jro ∪ dom gstore3, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, jro1.keys.inodes?, p_os.keys.inodes?, fi1.inos < pmaxino, ri0.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, ri0[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri0)].keys, ax0].inos < jmaxino0, jro1 < jmaxino0, inv(gstore2 \ jro0), inv(gstore1), inv(groupblock(gndx0, lax, m0)), inv(gstore3 \ jro), log-cons(abs-log(nx1, gstore2 ↓), nodes(gstore2 ↓, jro0)), new(ax0, nodes(gstore2 ↓, jro0)), refsize-cons(gstore3 -- n1, (range ri0 \ (range ri0 | n1)) ∪ ax0.toSet), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range ri0), refsize-cons(gstore3, (range ri0 \ (range ri0 | n1)) ∪ ax0.toSet), ri-cons(ri0, nodes(gstore2 ↓, jro0)), ri-inj(fi1), ri-inj(ri0[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri0)].keys, ax0]), ri-inj(ri0), n1 ∈ jro ∪ dom gstore3, n1 ∈ gstore3, n1 ∈ gstore1, n1 ∈ gstore2, pmaxino ≤ jmaxino, jmaxino ≤ jmaxino0, pmaxino ≤ jmaxino0, range ri0 ⊆ dom nodes(gstore2 ↓, jro0), fi1.lebs ⊆ dom gstore1, ri0.lebs ⊆ dom gstore2, dom gstore2 ⊆ dom gstore3, ri0[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri0)].keys, ax0].lebs ⊆ dom gstore3, ri0.lebs ⊆ dom gstore3, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3 -- n1, jro ++ n1), jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3, jro), jvalid3 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), jvalid5 → jvalid4 ⊦ #((dom nodes(gstore3 ↓, jro) | n1) ∩ ((range ri0 \ (range ri0 | n1)) ∪ ax0.toSet)) = 0, #(jro ∪ dom gstore3) = 0, jmaxino = 0, jmaxino0 = 0, m0 = 0, pmaxino = 0, (dom nodes(gstore3 ↓, jro) | n1) ∩ ((range ri0 \ (range ri0 | n1)) ∪ ax0.toSet) = ∅, jro ∪ dom gstore3 = ∅, dups(nx1), dups(nx0), dups(ax0), dups(nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri0)].keys), n1 ∈ nx1, n1 ∈ nx0, n1 ∈ jro0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 213:
# gstore2[n1].ladrlist = # gndx0, # ax0 = # referenced-adrs(gstore2[n1].ladrlist.to-adr(n1), ri0), gstore2[n1] = groupblock(gndx0, gstore2[n1].ladrlist, m0), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓) + ax0, nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[ax0, nodes(gstore2 ↓, jro0)[referenced-adrs(gstore2[n1].ladrlist.to-adr(n1), ri0)]], remove-refsize0(gstore1) = gstore1, elems nx1 ∩ jro0 = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx0 ∩ jro = ∅, dom gstore1 ∪ elems nx0 = jro ∪ dom gstore3, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, jro1.keys.inodes?, p_os.keys.inodes?, fi1.inos < pmaxino, ri0.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, ri0[nodes(gstore2 ↓, jro0)[referenced-adrs(gstore2[n1].ladrlist.to-adr(n1), ri0)].keys, ax0].inos < jmaxino0, jro1 < jmaxino0, inv(gstore2 \ jro0), inv(gstore1), inv(gstore2[n1]), inv(gstore3 \ jro), log-cons(abs-log(nx1, gstore2 ↓), nodes(gstore2 ↓, jro0)), new(ax0, nodes(gstore2 ↓, jro0)), refsize-cons(gstore3 -- n1, (range ri0 \ (range ri0 | n1)) ∪ ax0.toSet), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range ri0), refsize-cons(gstore3, (range ri0 \ (range ri0 | n1)) ∪ ax0.toSet), ri-cons(ri0, nodes(gstore2 ↓, jro0)), ri-inj(fi1), ri-inj(ri0[nodes(gstore2 ↓, jro0)[referenced-adrs(gstore2[n1].ladrlist.to-adr(n1), ri0)].keys, ax0]), ri-inj(ri0), n1 ∈ jro ∪ dom gstore3, n1 ∈ gstore3, n1 ∈ gstore1, n1 ∈ gstore2, pmaxino ≤ jmaxino, jmaxino ≤ jmaxino0, pmaxino ≤ jmaxino0, range ri0 ⊆ dom nodes(gstore2 ↓, jro0), fi1.lebs ⊆ dom gstore1, ri0.lebs ⊆ dom gstore2, dom gstore2 ⊆ dom gstore3, ri0[nodes(gstore2 ↓, jro0)[referenced-adrs(gstore2[n1].ladrlist.to-adr(n1), ri0)].keys, ax0].lebs ⊆ dom gstore3, ri0.lebs ⊆ dom gstore3, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3 -- n1, jro ++ n1), jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3, jro), jvalid3 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), jvalid5 → jvalid4 ⊦ #((dom nodes(gstore3 ↓, jro) | n1) ∩ ax0.toSet) = 0, #(jro ∪ dom gstore3) = 0, jmaxino = 0, jmaxino0 = 0, m0 = 0, pmaxino = 0, (dom nodes(gstore3 ↓, jro) | n1) ∩ ax0.toSet = ∅, jro ∪ dom gstore3 = ∅, dups(nx1), dups(nx0), dups(ax0), dups(nodes(gstore2 ↓, jro0)[referenced-adrs(gstore2[n1].ladrlist.to-adr(n1), ri0)].keys), 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]%size-zero: ⊦ # as ≠ 0 → 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%int-c: ⊦ as ∩ as0 = as0 ∩ as; from specification set-union[node-store]%int-a: ⊦ (as ∩ as0) ∩ as1 = as ∩ as0 ∩ as1; from specification set-union[node-store]%unc: ⊦ as ∪ as0 = as0 ∪ as; from specification set-union[node-store]%una: ⊦ (as ∪ as0) ∪ as1 = as ∪ as0 ∪ as1; from specification set-union[node-store]% ⊦ (as0 | n) ∩ ((as1 \ (as1 | n)) ∪ as2) = (as0 | n) ∩ as2; (s)