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Proof step 71 from proof refine-check-commit (previous step)

remove-refsize0(gstore1) = gstore1, elems nx ∩ jro2 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro2, jro1.keys.inodes?, p_os.keys.inodes?, jro1 < jmaxino, p_os < pmaxino, ri.inos < jmaxino, fi1.inos < pmaxino, inv(gstore2 \ jro2), inv(gstore1), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro2)), refsize-cons(gstore2, range ri), refsize-cons(gstore1, range fi1), ri-cons(ri, nodes(gstore2 ↓, jro2)), ri-inj(ri), ri-inj(fi1), pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, jvalid → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro2) ⊦ #(dom remove-refsize0(gstore2) ∩ jro2) = 0, jmaxino = 0, pmaxino = 0, dups(nx), ∀ n. n ∈ dom remove-refsize0(gstore2) ∩ jro2 ↔ n ∈ ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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 ∈ remove-refsize0(gstore) ↔ n ∈ gstore ∧ gstore[n].ref-size ≠ 0; (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]% ⊦ n ∈ dom gstore ↔ n ∈ gstore; (s)% ⊦ n ∈ ns ∩ ns0 ↔ n ∈ ns ∧ n ∈ ns0; (ws)% ⊦ ¬ n ∈ ∅; (s)