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Results tagged with calculus-of-inductive-constructions
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Calculus of (co)Inductive Constructions is a pure type system (Coquand, Huet) equipped with addition types: arbitrary (co)inductive types implementing general (co)inductive schemes; universes as a cumulative hierarchy of predicative types of types; and an impredicative type of propositions.
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How to prove in Lean that sums are distributive?
Assume we are given three types in Lean.
constants A B C : Type
There is a canonical map of the following form.
definition can : sum (A × B) (A × C) → A × (sum B C) :=
λ x , sum.cases_on x (λ y : …
- 971
2
votes
How to prove in Lean that sums are distributive?
I have figured out how to write the inverse using @sum.cases_on. The rules of @sum.cases_on in lean are nearly identical as the rules of match in Jacobs book. The code is:
definition can (α : Type) (β …
- 732