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Proof step 2 from proof inv-add-gnds (previous step)

inv-journal(nx, gstore, gstore0, ginval), ri-inj(fi0), ri-inj(fi) ⊦ ⟪index_add_gnds#(gndx, fi, fi0, ginval, gstore0, nx, maxino, ginval0; ax, gstore; syn, err)⟫ inv-journal(nx, gstore, gstore0, ginval), nx = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
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, maxino, ginval0; ax, gstore; syn, err)⟫ (inv(gstore \ ginval) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval)

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)