Strict order equational reasoning #1203
Merged
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Facilities for equational reasoning involving mixed use of
<
,≤
,≡
in a type that is both a quoset and a poset (with the additional data of<-≤-trans
,≤-<-trans
) to obtain a strict inequality (having at least a<
in the chain).This is inspired from
Relation.Binary.Reasoning.PartialOrder
of the Agda Standard Library.Some notes:
Such a chain can be written without nested equations, but it is not recomended, since it will perform a bunch of
subst
s, and the combinators from Prelude (such as_ ≡[ i ]⟨ p i ⟩ _
) cannot be used.begin
is needed at the start of the chain, since it has to extract a strict inequality from the given chain.<
won't be required in the chain.