What is Local Reasoning , exactly?

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

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(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.