What is Local Reasoning , exactly?

Question

What is Local Reasoning? how does it relate to Referential Transparency, Equational Reasoning and Laziness?

Answer 1

(adding the definition from the commented link, just to avoid link only answer )

From http://degoes.net/articles/fp-glossary

Local reasoning is a property of some code wherein the correctness of the code can be inferred locally under specified assumptions, without considering prior application state or all possible inputs.