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Proof step 125 from proof inv-gc (previous step)

# lax = # gndx0, # ax = # referenced-adrs(lax.to-adr(n1), fi2), gndx.last = mkgnode(nd, m1, boolvar, boolvar0), gstore2[n1] = groupblock(gndx0, lax, m0), gstore3[nx0.last] = groupblock(gndx, lax0, m), 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(groupblock(gndx, lax0, m)), 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, n1 ∈ dom gstore3 ∪ jro, nx0.last ∈ gstore3, 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), gndx = [] ∨ boolvar0 ⊦ #(dom gstore3 ∪ jro) = 0, jmaxino = 0, jmaxino0 = 0, m0 = 0, nx0 = [], pmaxino = 0, dom gstore3 ∪ jro = ∅, dups(nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys), dups(nx0), dups(ax), dups(nx1), valid-journal-head(nx0, gstore3 -- n1, jro ++ n1), n1 ∈ nx0, n1 ∈ jro0, n1 ∈ nx1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: gjournal-base name: valid-journal-head seq: ⊦ valid-journal-head(nx, gstore, ginval) ↔ nx ≠ [] ∧ nx.last ∈ gstore ∧ ¬ nx.last ∈ ginval ∧ ( gstore[nx.last].gndlist = [] ∨ gstore[nx.last].gndlist.last.end) subst: [ginval, gstore, nx] → [jro ++ n1, gstore3 -- n1, nx0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n ∈ gstore -- n0 ↔ n ≠ n0 ∧ n ∈ gstore; (s)% ⊦ n ≠ n0 → (n ∈ ns ++ n0 ↔ n ∈ ns); (s)%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]%int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set]% ⊦ elems nx ∩ ginval = ∅ ∧ nx ≠ [] → ¬ nx.last ∈ ginval; (s)% ⊦ n ≠ n0 → (gstore -- n0)[n] = gstore[n]; (s)% ⊦ groupblock(gndx, lax, m).gndlist = gndx; (s)% ⊦ nx.last ∈ nx ↔ nx ≠ []; (s)% ⊦ mkgnode(nd, m, boolvar, boolvar0).end ↔ boolvar0; (s) Used terms: jro ++ n1, gstore3 -- n1, nx0