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Proof step 8 from proof fwd-inv-loghead (previous step)

(elems nx0 ∪ dom gstore0) ++ n = dom gstore ∪ ginval, ginval ∩ elems nx0 = ∅, n ∈ gstore \ ginval → inv((gstore \ ginval)[n]) ⊦ inv(gstore[n]), n ∈ ginval

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
(elems nx0 ∪ dom gstore0) ++ n = dom gstore ∪ ginval, ginval ∩ elems nx0 = ∅ ⊦ inv((∅)[n]), n ∈ gstore, n ∈ ginval

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ n ∈ gstore → gstore[n] = (∅)[n]; (s)% ⊦ ¬ n ∈ ns → (gstore \ ns)[n] = gstore[n]; (s)% ⊦ n ∈ gstore \ ns ↔ n ∈ gstore ∧ ¬ n ∈ ns; (ws)