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Proof step 188 from proof inv-gc (previous step)

gstore2[n1] = groupblock(gndx, lax, 0), err0 = ESUCCESS, 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, pmaxino ≤ jmaxino, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, jvalid4 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ jmaxino = 0, pmaxino = 0, dups(nx), n1 ∈ nx, (jvalid4 ∧ nx ≠ [] → valid-journal-head(nx, gstore2 -- n1, jro0 ++ n1)) ∧ fi2.lebs ⊆ dom(gstore2 -- n1) ∧ refsize-cons(gstore2 -- n1, range fi2) ∧ inv((gstore2 -- n1) \ (jro0 ++ n1)) ∧ elems nx ∩ (jro0 ++ n1) = ∅ ∧ dom gstore1 ∪ elems nx = dom(gstore2 -- n1) ∪ (jro0 ++ n1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 189:
gstore2[n1] = groupblock(gndx, lax, 0), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, fi1.inos < pmaxino, fi2.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, inv(gstore1), inv(gstore2 \ jro0), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range fi2), ri-cons(fi2, nodes(gstore2 ↓, jro0)), ri-inj(fi1), ri-inj(fi2), n1 ∈ dom gstore2 ∪ jro0, n1 ∈ gstore1, n1 ∈ gstore2, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, fi2.lebs ⊆ dom gstore2, jvalid4 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ #(dom gstore2 ∪ jro0) = 0, jmaxino = 0, pmaxino = 0, dom gstore2 ∪ jro0 = ∅, dups(nx), n1 ∈ nx, (adr.lnum ≠ n1 ∨ ¬ adr ∈ fi2) ∧ (jvalid4 ∧ nx ≠ [] → valid-journal-head(nx, gstore2 -- n1, jro0 ++ 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)