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Fix some min that were replaced by inf.
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PatrickMassot committed Jan 31, 2023
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Expand Up @@ -75,7 +75,7 @@ has the properties indicated.
A *lattice* is a structure that extends a partial
order with operations ``⊓`` and ``⊔`` that are
analogous to ``inf`` and ``max`` on the real numbers:
analogous to ``min`` and ``max`` on the real numbers:
TEXT. -/
-- BOTH:
section
Expand Down Expand Up @@ -106,15 +106,15 @@ theorem names.
To further complicate matters,
they are also often called *meet* and *join*.
Therefore, if you work with lattices,
you have to keep the following dictionary in infd:
you have to keep the following dictionary in mind:
* ``⊓`` is the *greatest lower bound*, *infimum*, or *meet*.
* ``⊔`` is the *least upper bound*, *supremum*, or *join*.
Some instances of lattices include:
* ``inf`` and ``max`` on any total order, such as the integers or real numbers with ``≤``
* ``min`` and ``max`` on any total order, such as the integers or real numbers with ``≤``
* ``∩`` and ``∪`` on the collection of subsets of some domain, with the ordering ``⊆``
Expand All @@ -133,7 +133,7 @@ Some instances of lattices include:
the least upper bound is their intersection,
and the ordering is reverse inclusion
You can check that, as with ``inf`` / ``max`` and ``gcd`` / ``lcm``,
You can check that, as with ``min`` / ``max`` and ``gcd`` / ``lcm``,
you can prove the commutativity and associativity of the infimum and supremum
using only their characterizing axioms,
together with ``le_refl`` and ``le_trans``.
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