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Proof step 5 from proof write-dom (previous step)

# ax0 = # ndx0, ∀ ndx, fs. # ndx0 = # ndx → dom fs[ax0, ndx] = dom fs ∪ ax0.toSet ⊦ dom fs[adr, nd][ax0, ndx0] = (ax0.toSet ∪ dom fs) ++ adr

User applied rule all left

And closed the goal!

Rule argument

pos: left 2 terms: ndx0, fs[adr, nd] abort: F discard: T computed: T

Additional information

Used simplifier rules: ⊦ dom fs[adr, nd] = dom fs ++ adr; (s)% ⊦ (as ++ adr) ∪ as0 = (as ∪ as0) ++ adr; (s)%una: ⊦ (as ∪ as0) ∪ as1 = as ∪ as0 ∪ as1; from specification set-union[node-store]%unc: ⊦ as ∪ as0 = as0 ∪ as; from specification set-union[node-store] Used terms: ndx0, fs[adr, nd]