well-founded

adjective3

1. •
   Based on reasoning, evidence and good judgement.
2. •
   Properly substantiated.

   • After the crisis had passed, certain well-founded proposals were revived, and resulted in important additions to the railway network of the country. — 1946
3. •
   Of a binary relation: such that every non-empty subset of the relation's domain has a minimal element with respect to the relation.

   • well-founded relation