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Proof step 2 from proof crash-neutral-add-gnds (previous step)

fi1 = fi0, ginval0 = ginval, ginval1 = ginval2, gstore1 = crash(gstore, gstore0, ginval, nx), gstore2 = gstore0, maxino = maxino0, nx0 = nx, syn, inv-journal(nx, gstore, gstore0, ginval), ri-inj(fi0), ri-inj(fi) ⊦ ⟨index_add_gnds#(gndx, fi, fi0, ginval, gstore0, nx, maxino0, ginval2; ax, gstore; syn, err)⟩ ( syn ∧ ginval0 = ginval ∧ gstore1 = crash(gstore, gstore0, ginval, nx) ∧ gstore2 = gstore0 ∧ nx0 = nx ∧ maxino = maxino0 ∧ ginval1 = ginval2 ∧ fi1 = fi0), nx = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
gstore1 = crash(gstore, gstore0, ginval, nx), remove-refsize0(gstore0) = gstore0, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, nx ≠ [], inv(gstore \ ginval), inv(gstore0), inv(gstore[nx.last]), ri-inj(fi), ri-inj(fi0), nx.last ∈ gstore, ¬ dups(nx) ⊦ ⟨index_add_gnds#(gndx, fi, fi0, ginval, gstore0, nx, maxino0, ginval2; ax, gstore; syn, err)⟩ (syn ∧ gstore1 = crash(gstore, gstore0, ginval, nx))

Rule argument

Additional information

Used simplifier rules: fwd-inv-loghead: ⊦ nx ≠ [] ∧ inv(gstore \ ginval) ∧ ginval ∩ elems nx = ∅ ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval → inv(gstore[nx.last]); (forward) from specification apersistence-base%fwd-in-gstore-loghead: ⊦ nx ≠ [] ∧ ginval ∩ elems nx = ∅ ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval → nx.last ∈ gstore; (forward) from specification apersistence-base%unc: ⊦ ns ∪ ns0 = ns0 ∪ ns; from specification set-union[nat-set]%una: ⊦ (ns ∪ ns0) ∪ ns1 = ns ∪ ns0 ∪ ns1; from specification set-union[nat-set]%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]%⊦ 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)