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Proof step 190 from proof inv-gc (previous step)

gstore2[n1] = groupblock(gndx, lax, 0), adr = @(m, m0, m1), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, jro1 < jmaxino, p_os < pmaxino, fi2.inos < jmaxino, fi1.inos < pmaxino, inv(gstore2 \ jro0), inv(gstore1), refsize-cons(gstore2, range fi2), refsize-cons(gstore1, range fi1), ri-cons(fi2, nodes(gstore2 ↓, jro0)), ri-inj(fi2), ri-inj(fi1), n1 ∈ gstore2, n1 ∈ gstore1, n1 ∈ dom gstore2 ∪ jro0, pmaxino ≤ jmaxino, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, jvalid4 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ #(dom gstore2 ∪ jro0) = 0, jmaxino = 0, pmaxino = 0, dom gstore2 ∪ jro0 = ∅, dups(nx), n1 ∈ nx, (m ≠ n1 ∨ ¬ adr ∈ fi2) ∧ (jvalid4 ∧ nx ≠ [] → valid-journal-head(nx, gstore2 -- n1, jro0 ++ n1))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 191:
gstore2[n1] = groupblock(gndx, lax, 0), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, jro1 < jmaxino, p_os < pmaxino, fi2.inos < jmaxino, fi1.inos < pmaxino, inv(gstore2[nx.last]), inv(gstore2 \ jro0), inv(gstore1), refsize-cons(gstore2, range fi2), refsize-cons(gstore1, range fi1), ri-cons(fi2, nodes(gstore2 ↓, jro0)), ri-inj(fi2), ri-inj(fi1), valid-journal-head(nx, gstore2, jro0), nx.last ∈ gstore2, n1 ∈ gstore2, n1 ∈ gstore1, n1 ∈ dom gstore2 ∪ jro0, pmaxino ≤ jmaxino, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1 ⊦ #(dom gstore2 ∪ jro0) = 0, jmaxino = 0, nx = [], pmaxino = 0, dom gstore2 ∪ jro0 = ∅, dups(nx), valid-journal-head(nx, gstore2 -- n1, jro0 ++ n1), n1 ∈ nx

Rule argument

Additional information

Used simplifier rules: fwd-inv-loghead: ⊦ nx ≠ [] ∧ inv(gstore \ ginval) ∧ ginval ∩ elems nx = ∅ ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval → inv(gstore[nx.last]); (forward) from specification apersistence-base%fwd-in-gstore-loghead: ⊦ nx ≠ [] ∧ ginval ∩ elems nx = ∅ ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval → nx.last ∈ 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]%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]%⊦ gstore[n] = groupblock(gndx, lax, 0) ∧ n ∈ gstore ∧ ri-cons(ri, nodes(gstore ↓, ginval)) ∧ refsize-cons(gstore, range ri) ∧ inv(gstore \ ginval) → ¬ @(n, m0, m1) ∈ ri; (s)