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Proof step 3 from proof write-dom (previous step)

# 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

User applied rule constructor cut

And obtained the following new goals

Proof step 4:
# ax0 + 1 = # ndx, ndx = nd + ndx0, ∀ ndx, fs. # ax0 = # ndx → dom fs[ax0, ndx] = dom fs ∪ ax0.toSet ⊦ dom fs[adr ' + ax0, ndx] = (ax0.toSet ∪ dom fs) ++ adr

Rule argument

var: ndx

Additional information

Used simplifier rules: node-list freely generated by [], +;;% ⊦ # [] = 0; (s)% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)% ⊦ # ax = 0 ↔ ax = []; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic