fix(doc): fix confusion between Prop and Bool
this fix assumes that Prop and Bool are two different things but even if they were the same thing, using the two names would only confuse the reader
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@ -709,7 +709,7 @@ for =∃ a : nat, a = w= using
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Note that =exists.intro= also has implicit arguments. For example, Lean has to infer the implicit argument
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Note that =exists.intro= also has implicit arguments. For example, Lean has to infer the implicit argument
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=P : A → Bool=, a predicate (aka function to Prop). This creates complications. For example, suppose
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=P : A → Prop=, a predicate (aka function to Prop). This creates complications. For example, suppose
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we have =Hg : g 0 0 = 0= and we invoke =exists.intro 0 Hg=. There are different possible values for =P=.
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we have =Hg : g 0 0 = 0= and we invoke =exists.intro 0 Hg=. There are different possible values for =P=.
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Each possible value corresponds to a different theorem: =∃ x, g x x = x=, =∃ x, g x x = 0=,
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Each possible value corresponds to a different theorem: =∃ x, g x x = x=, =∃ x, g x x = 0=,
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=∃ x, g x 0 = x=, etc. Lean uses the context where =exists.intro= occurs to infer the users intent.
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=∃ x, g x 0 = x=, etc. Lean uses the context where =exists.intro= occurs to infer the users intent.
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