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

fi0.inos < pmaxino, fi.inos < jmaxino, p_os < pmaxino, jro < jmaxino, inv-journal(nx, gstore, gstore0, jro0), refsize-cons(gstore0, range fi0), refsize-cons(gstore, range fi), ri-cons(fi, nodes(gstore ↓, jro0)), ri-inj(fi0), ri-inj(fi), pmaxino ≤ jmaxino, fi0.lebs ⊆ dom gstore0, fi.lebs ⊆ dom gstore, jvalid ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0) ⊦ ⟪gjournal_journal_gc#(jvalid0, fi0, gstore0, pmaxino, p_os; jvalid, jmaxino0, jmaxino, fi, jro0, gstore, nx, jvalid1)⟫ ( jro < jmaxino ∧ pmaxino ≤ jmaxino ∧ fi.inos < jmaxino ∧ jmaxino ≠ 0 ∧ (jvalid ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0)) ∧ fi.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi) ∧ inv-journal(nx, gstore, gstore0, jro0) ∧ ri-inj(fi)), jmaxino = 0, pmaxino = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
remove-refsize0(gstore0) = gstore0, elems nx ∩ jro0 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, jmaxino ≠ 0, pmaxino ≠ 0, jro < jmaxino, p_os < pmaxino, fi.inos < jmaxino, fi0.inos < pmaxino, inv(gstore \ jro0), inv(gstore0), refsize-cons(gstore, range fi), refsize-cons(gstore0, range fi0), ri-cons(fi, nodes(gstore ↓, jro0)), 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, jro0) ⊦ ⟪gjournal_journal_gc#(jvalid0, fi0, gstore0, pmaxino, p_os; jvalid, jmaxino0, jmaxino, fi, jro0, gstore, nx, jvalid1)⟫ ( jro < jmaxino ∧ pmaxino ≤ jmaxino ∧ fi.inos < jmaxino ∧ jmaxino ≠ 0 ∧ (jvalid ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0)) ∧ fi.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi) ∧ inv(gstore \ jro0) ∧ elems nx ∩ jro0 = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ jro0 ∧ ri-inj(fi))

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)