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Proof step 2 from proof write-dom (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
# ax0 + 1 = # ndx, ∀ ndx, fs. # ax0 = # ndx → dom fs[ax0, ndx] = dom fs ∪ ax0.toSet ⊦ dom fs[adr ' + ax0, ndx] = (ax0.toSet ∪ dom fs) ++ adr

Rule argument

Additional information

Used simplifier rules: unc: ⊦ as ∪ as0 = as0 ∪ as; from specification set-union[node-store]%una: ⊦ (as ∪ as0) ∪ as1 = as ∪ as0 ∪ as1; from specification set-union[node-store]% ⊦ as ∪ ∅ = as; (s)% ⊦ (as ++ adr) ∪ as0 = (as ∪ as0) ++ adr; (s)% ⊦ adr '.toSet = ∅ ++ adr; (s)% ⊦ (ax + ax0).toSet = ax.toSet ∪ ax0.toSet; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ m +1 = m + 1; (s)% ⊦ #(adr ' + ax) = (# ax)+1; (s)% ⊦ adr + ax = adr ' + ax; (s)