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Warn about non-commutative StrictOrderedRing
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PatrickMassot committed Nov 11, 2024
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/- TEXT:
It is possible to combine axiomatic structures into larger ones.
For example, a *strict ordered ring* consists of a commutative ring together
For example, a *strict ordered ring* consists of a ring together
with a partial order on the carrier
satisfying additional axioms that say that the ring operations
are compatible with the order:
Expand Down Expand Up @@ -353,7 +353,8 @@ used to reason about arithmetic and the ordering on the real
numbers hold generically for any ordered ring.
Here are a couple of examples you can try,
using only properties of rings, partial orders, and the facts
enumerated in the last two examples:
enumerated in the last two examples (beware that those rings are
not assumed to be commutative, so the `ring` tactic is not available):
TEXT. -/
-- QUOTE:
example (h : a ≤ b) : 0 ≤ b - a := by
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