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Proof step 41 from proof inv-recover (previous step)

n ∈ dom gstore3 ∪ elems nx3 ↔ n ∈ dom gstore2 ∪ jro3, remove-refsize0(gstore3) = gstore3, elems nx3 ∩ jro3 = ∅, jro2 < jmaxino3, jro5 < jmaxino0, fi1.inos < jmaxino3, fi4.inos < jmaxino0, inv(gstore2 \ jro3), inv(gstore3), refsize-cons(gstore2, range fi1), refsize-cons(gstore3, range fi4), ri-inj(fi1), ri-inj(fi4), n ∈ jro3, jmaxino0 ≤ jmaxino3, fi1.lebs ⊆ dom gstore2, fi4.lebs ⊆ dom gstore3, jvalid0 ∧ nx3 ≠ [] → valid-journal-head(nx3, gstore2, jro3) ⊦ # jro3 = 0, jmaxino0 = 0, jmaxino3 = 0, jro3 = ∅, dups(nx3), inv(gstore3[n]), n ∈ nx3

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
remove-refsize0(gstore3) = gstore3, elems nx3 ∩ jro3 = ∅, fi4.inos < jmaxino0, fi1.inos < jmaxino3, jro5 < jmaxino0, jro2 < jmaxino3, inv(gstore3), inv(gstore2 \ jro3), refsize-cons(gstore3, range fi4), refsize-cons(gstore2, range fi1), ri-inj(fi4), ri-inj(fi1), n ∈ dom gstore2 ∪ jro3, n ∈ dom gstore3 ∪ elems nx3, n ∈ jro3, jmaxino0 ≤ jmaxino3, fi4.lebs ⊆ dom gstore3, fi1.lebs ⊆ dom gstore2, jvalid0 ∧ nx3 ≠ [] → valid-journal-head(nx3, gstore2, jro3) ⊦ # jro3 = 0, #(dom gstore2 ∪ jro3) = 0, #(dom gstore3 ∪ elems nx3) = 0, jmaxino0 = 0, jmaxino3 = 0, jro3 = ∅, dom gstore2 ∪ jro3 = ∅, dom gstore3 ∪ elems nx3 = ∅, dups(nx3), inv(gstore3[n]), n ∈ nx3

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]%unc: ⊦ ns ∪ ns0 = ns0 ∪ ns; from specification set-union[nat-set]%una: ⊦ (ns ∪ ns0) ∪ ns1 = ns ∪ ns0 ∪ ns1; from specification set-union[nat-set]% ⊦ n ∈ dom gstore ↔ n ∈ gstore; (s)% ⊦ n ∈ ns ∪ ns0 ↔ ¬(¬ n ∈ ns ∧ ¬ n ∈ ns0); (ss)