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Proof step 98 from proof inv-gc (previous step)

# lax = # gndx0, # ax = # referenced-adrs(lax.to-adr(n1), fi2), gstore2[n1] = groupblock(gndx0, lax, m0), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓) + ax, err0 = ESUCCESS, nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[ax, nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)]], remove-refsize0(gstore1) = gstore1, elems nx0 ∩ jro = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx1 ∩ jro0 = ∅, dom gstore1 ∪ elems nx0 = dom gstore3 ∪ jro, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, jro1 < jmaxino0, fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax].inos < jmaxino0, fi1.inos < pmaxino, fi2.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, inv(gstore3 \ jro), inv(gstore2 \ jro0), inv(gstore1), inv(groupblock(gndx0, lax, m0)), new(ax, nodes(gstore2 ↓, jro0)), refsize-cons(gstore3, range fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax]), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range fi2), ri-cons(fi2, nodes(gstore2 ↓, jro0)), ri-inj(fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax]), ri-inj(fi1), ri-inj(fi2), n1 ∈ gstore3, n1 ∈ gstore2, n1 ∈ gstore1, pmaxino ≤ jmaxino0, jmaxino ≤ jmaxino0, pmaxino ≤ jmaxino, fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax].lebs ⊆ dom gstore3, dom gstore2 ⊆ dom gstore3, range fi2 ⊆ dom nodes(gstore2 ↓, jro0), fi1.lebs ⊆ dom gstore1, fi2.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore3, jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3, jro), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ jmaxino = 0, jmaxino0 = 0, m0 = 0, pmaxino = 0, dups(nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys), dups(nx0), dups(ax), dups(nx1), n1 ∈ nx0, n1 ∈ jro0, n1 ∈ nx1, (jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3 -- n1, jro ++ n1)) ∧ fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax].lebs ⊆ dom(gstore3 -- n1) ∧ refsize-cons(gstore3 -- n1, range fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax]) ∧ inv((gstore3 -- n1) \ (jro ++ n1)) ∧ elems nx0 ∩ (jro ++ n1) = ∅ ∧ dom gstore1 ∪ elems nx0 = dom(gstore3 -- n1) ∪ (jro ++ n1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 99:
# ax = # referenced-adrs(lax.to-adr(n1), fi2), # lax = # gndx0, 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[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax]), 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 ∈ dom gstore3 ∪ jro, n1 ∈ gstore1, n1 ∈ gstore2, n1 ∈ gstore3, 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) ⊦ #(dom gstore3 ∪ jro) = 0, jmaxino = 0, jmaxino0 = 0, m0 = 0, pmaxino = 0, dom gstore3 ∪ jro = ∅, dups(nx1), dups(ax), dups(nx0), dups(nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys), n1 ∈ nx1, n1 ∈ jro0, n1 ∈ nx0, (adr.lnum ≠ n1 ∨ ¬ adr ∈ fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(adr.lnum), fi2)].keys, ax]) ∧ (jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3 -- n1, jro ++ n1))

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ ns ≠ ∅ → # ns ≠ 0; (forward) from specification set-basic[nat-set]%ne-01: ⊦ n ∈ ns → ns ≠ ∅; (forward) from specification set-basic[nat-set]% ⊦ n ∈ dom gstore ↔ n ∈ gstore; (s)% ⊦ n ∈ ns ∪ ns0 ↔ ¬(¬ n ∈ ns ∧ ¬ n ∈ ns0); (ss)% ⊦ ns ++ n = ns ↔ n ∈ ns; (s)%unc: ⊦ ns ∪ ns0 = ns0 ∪ ns; from specification set-union[nat-set]%una: ⊦ (ns ∪ ns0) ∪ ns1 = ns ∪ ns0 ∪ ns1; from specification set-union[nat-set]% ⊦ (ns ∪ (ns0 -- n)) ++ n = (ns ∪ ns0) ++ n; (s)% ⊦ (ns ++ n) ∪ ns0 = (ns ∪ ns0) ++ n; (s)% ⊦ n ∈ elems nx ↔ n ∈ nx; (s)% ⊦ ns ∩ (ns0 ++ n) = ∅ ↔ ns ∩ ns0 = ∅ ∧ ¬ n ∈ ns; (ws)%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]% ⊦ inv(gstore \ ns) → inv(gstore \ (ns ++ n)); (s)% ⊦ n ∈ gstore → (gstore \ (ns ++ n)) -- n = gstore \ (ns ++ n); (s)% ⊦ (gstore -- n) \ ns = (gstore \ ns) -- n; (s)% ⊦ refsize-cons(gstore, as) → refsize-cons(gstore -- n, as); (ss)% ⊦ n ∈ ri.lebs ↔ (∃ adr. adr.lnum = n ∧ adr ∈ ri); (s)% ⊦ ns ⊆ ns0 -- n ↔ ns ⊆ ns0 ∧ ¬ n ∈ ns; (ws)% ⊦ dom(gstore -- n) = dom gstore -- n; (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)