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Proof step 135 from proof inv-gc (previous step)

# 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 ∈ gstore1, 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), 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), n1 ∈ gstore2 → n1 ∈ gstore3 ⊦ 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 ∈ jro0, n1 ∈ nx1, n1 ∈ gstore3 ∧ ¬ n1 ∈ nx0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 136:
# 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, 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 ∈ gstore2, n1 ∈ gstore1, n1 ∈ nx0, n1 ∈ gstore3, pmaxino ≤ jmaxino0, jmaxino ≤ jmaxino0, pmaxino ≤ jmaxino, fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax].lebs ⊆ 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) ⊦ jmaxino = 0, jmaxino0 = 0, m0 = 0, pmaxino = 0, dups(nx1), dups(ax), dups(nx0), dups(nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys), n1 ∈ nx1, n1 ∈ jro0, n1 ∈ jro

Rule argument

Additional information

Used simplifier rules: fwd-in-log-in-gstore: ⊦ n ∈ nx ∧ ginval ∩ elems nx = ∅ ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval → n ∈ 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]%elems-in-notin-ginval: ⊦ n ∈ nx ∧ elems nx ∩ ns = ∅ → ¬ n ∈ ns; (forward) from specification apersistence-base%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]