(formula_7 is any node whose best path to the goal, of length m+1, goes through some immediate child formula_8 whose best path to the goal is of length m.)

Consistent heuristics are called monotone because the estimated final cost of a partial solution, formula_9 is monotonically non-decreasing along the best path to the goal, where formula_10 is the cost of the best path from start node formula_11 to formula_12.