Proposed is a form of Propose. Propose is related to Will. Could is etymologically related to Will. Could is etymologically related to Should. 
Undertake is a type of Initiate. Establish is a type of Initiate. Establish is a synonym of Prove. Prove is derived from Proof. 
Proposed --FormOf--> Propose <--RelatedTo--> Will <--EtymologicallyRelatedTo-- Could --EtymologicallyRelatedTo--> Should 
Undertake --IsA--> Initiate <--IsA-- Establish <--Synonym--> Prove --DerivedFrom--> Proof 