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Proof step 2 from proof crash-neutral-store (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), key-cons(key, gstore[adr].nd), ri-inj(fi0), ri-inj(fi), adr ∈ gstore ⊦ ⟨index_index_store#(key, adr, fi0, ginval, gstore, gstore0, nx, maxino0, ginval2, syn; adr0, syn0, fi)⟩ ( syn ∧ ginval0 = ginval ∧ gstore1 = crash(gstore, gstore0, ginval, nx) ∧ gstore2 = gstore0 ∧ nx0 = nx ∧ maxino = maxino0 ∧ ginval1 = ginval2 ∧ fi1 = fi0), adr ∈ fi

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, inv(gstore \ ginval), inv(gstore0), key-cons(key, gstore[adr].nd), ri-inj(fi), ri-inj(fi0), adr ∈ gstore, ¬ dups(nx), ¬ adr ∈ fi ⊦ ⟨index_index_store#(key, adr, fi0, ginval, gstore, gstore0, nx, maxino0, ginval2, true; adr0, syn0, fi)⟩ true

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)