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Proof step 16 from proof prepost-restore-log (previous step)

elems(nx0 + n ' + nx2) ∩ ginval = ∅, inv(gstore2 \ ginval), ∀ n0. n0 ∈ elems(nx0 + n ' + nx2) → n0 ∈ dom gstore2 ⊦ n ∈ gstore2 ∧ ¬ n ∈ ginval

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
elems(nx0 + n ' + nx2) ∩ ginval = ∅, inv(gstore2 \ ginval), ∀ n0. n0 ∈ nx0 ∨ n0 = n ∨ n0 ∈ nx2 → n0 ∈ gstore2 ⊦ n ∈ gstore2 ∧ ¬ n ∈ ginval

Rule argument

Additional information

Used simplifier rules: ⊦ n ∈ dom gstore ↔ n ∈ gstore; (s)%a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]% ⊦ n ∈ n0 ' + nx ↔ n = n0 ∨ n ∈ nx; (s)% ⊦ n ∈ nx + nx0 ↔ n ∈ nx ∨ n ∈ nx0; (s)% ⊦ n ∈ elems nx ↔ n ∈ nx; (s)