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Proof step 38 from proof inv-recover (previous step)

remove-refsize0(gstore3) = gstore3, elems nx3 ∩ jro3 = ∅, dom gstore3 ∪ elems nx3 = dom gstore2 ∪ 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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 39:
⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0)
Proof step 40:
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 ∈ jro3, jmaxino0 ≤ jmaxino3, fi4.lebs ⊆ dom gstore3, fi1.lebs ⊆ dom gstore2, jvalid0 ∧ nx3 ≠ [] → valid-journal-head(nx3, gstore2, jro3), ∀ n. n ∈ dom gstore3 ∪ elems nx3 ↔ n ∈ dom gstore2 ∪ jro3 ⊦ # jro3 = 0, jmaxino0 = 0, jmaxino3 = 0, jro3 = ∅, dups(nx3), inv(gstore3[n]), n ∈ nx3

Rule argument

spec: set-basic, inst: nat-set name: Extension seq: ⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0) subst: [ns0, ns] → [dom gstore2 ∪ jro3, dom gstore3 ∪ elems nx3] flags: <all paths>

Additional information

Used terms: dom gstore2 ∪ jro3, dom gstore3 ∪ elems nx3