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Proof step 2 from proof inv-add5 (previous step)

fi0.inos < pmaxino, fi.inos < jmaxino, p_os < pmaxino, inv-journal(nx, gstore, gstore0, jro), refsize-cons(gstore0, range fi0), refsize-cons(gstore, range fi), ri-inj(fi0), ri-inj(fi), pmaxino ≤ jmaxino, fi0.lebs ⊆ dom gstore0, fi.lebs ⊆ dom gstore, jvalid ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro) ⊦ ⟪gjournal_journal_add5# (nd, nd0, nd1, nd2, nd3, jvalid0, fi, fi0, gstore0, pmaxino, p_os; adr, adr0, adr1, adr2, adr3, jvalid, jmaxino0, jro, gstore, nx, jvalid1; err)⟫ ( (jvalid ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro)) ∧ fi.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi) ∧ inv-journal(nx, gstore, gstore0, jro)), pmaxino = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
remove-refsize0(gstore0) = gstore0, elems nx ∩ jro = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro, pmaxino ≠ 0, p_os < pmaxino, fi.inos < jmaxino, fi0.inos < pmaxino, inv(gstore \ jro), inv(gstore0), refsize-cons(gstore, range fi), refsize-cons(gstore0, range fi0), ri-inj(fi), ri-inj(fi0), pmaxino ≤ jmaxino, fi.lebs ⊆ dom gstore, fi0.lebs ⊆ dom gstore0, ¬ dups(nx), jvalid ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro) ⊦ ⟪gjournal_journal_add5# (nd, nd0, nd1, nd2, nd3, jvalid0, fi, fi0, gstore0, pmaxino, p_os; adr, adr0, adr1, adr2, adr3, jvalid, jmaxino0, jro, gstore, nx, jvalid1; err)⟫ ( (jvalid ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro)) ∧ fi.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi) ∧ inv(gstore \ jro) ∧ elems nx ∩ jro = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ jro)

Rule argument

Additional information

Used simplifier rules: ⊦ inv-journal(nx, gstore, gstore0, ginval) ↔ inv(gstore \ ginval) ∧ inv(gstore0) ∧ elems nx ∩ ginval = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval ∧ remove-refsize0(gstore0) = gstore0; (s)