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Proof step 83 from proof inv-truncate (previous step)

jvalid0 ↔ jvalid2, as = as0, as1 = fi1[datakeys(key, n, fi1)], dom gstore = dom gstore4, fi = fi2, fi0 = fi1 \ datakeys(key, n, fi1), gstore0 = gstore1, gstore2 = gstore3, gstore4 = gstore3, remove-refsize0(gstore1) = gstore1, as ∩ range fi0 = ∅, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore3 ∪ jro, fi2.inos < pmaxino, fi1.inos < jmaxino, p_os < pmaxino, gstore =○refsize gstore4, inv(gstore1), inv(gstore3 \ jro), inv-journal(nx, gstore, gstore0, jro), refsize-cons(gstore, range fi0 ∪ as), refsize-cons(gstore1, range fi2), refsize-cons(gstore3, range fi1), ri-inj(fi2), ri-inj(fi1), ri-inj(fi1 \ datakeys(key, n, fi1)), pmaxino ≤ jmaxino, as.lebs ⊆ dom gstore, fi2.lebs ⊆ dom gstore1, fi1.lebs ⊆ dom gstore3, jvalid0 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro), jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro) ⊦ as = ∅, pmaxino = 0, dups(nx), ∃ n, adr. adr ∈ as

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 84:
dom gstore = dom gstore3, remove-refsize0(gstore1) = gstore1, as ∩ range(fi1 \ datakeys(key, n, fi1)) = ∅, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore3 ∪ jro, fi2.inos < pmaxino, fi1.inos < jmaxino, p_os < pmaxino, gstore =○refsize gstore3, inv(gstore \ jro), inv(gstore1), inv(gstore3 \ jro), refsize-cons(gstore, range(fi1 \ datakeys(key, n, fi1)) ∪ as), refsize-cons(gstore1, range fi2), refsize-cons(gstore3, range fi1), ri-inj(fi2), ri-inj(fi1), ri-inj(fi1 \ datakeys(key, n, fi1)), pmaxino ≤ jmaxino, as.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore1, fi1.lebs ⊆ dom gstore3, jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro), jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro) ⊦ # as = 0, as = ∅, pmaxino = 0, dups(nx), ∃ adr. adr ∈ as

Rule argument

Additional information

Used simplifier rules: size-zero: ⊦ # as ≠ 0 → as ≠ ∅; (forward) from specification set-basic[node-store]%size-zero-01: ⊦ as ≠ ∅ → # as ≠ 0; (forward) from specification set-basic[node-store]%⊦ 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)