def total_ordering(*relations):
'''
Return a conjunction of relations in the total ordering style.
For example, "a > b >= c = d > e" is a total ordering style for
"(a > b) and (b >= c) and (c = d) and (d > e)".
'''
from proveit.logic import And
conjunction = And(*relations)
conjunction = conjunction.with_total_ordering_style()
if conjunction.operands.is_single():
# A single relation is a trivial total ordering.
return conjunction.operands[0]
return conjunction
def total_ordering(*relations, prove=False):
'''
Return a conjunction of relations in the total ordering style.
For example, "a > b >= c = d > e" is a total ordering style for
"(a > b) and (b >= c) and (c = d) and (d > e)". If there is a
single relation, just return the relation. If 'prove' is True,
return a proven Judgment.
'''
from proveit import ExprRange
from proveit.logic import And
if len(relations) == 1 and not isinstance(relations[0], ExprRange):
# Return a trivial, singular relation.
relation = relations[0]
if prove: relation = relation.prove()
return relation
# Return a conjunction with the proper style.
conjunction = And(*relations)
conjunction = conjunction.with_total_ordering_style()
if prove:
# Prove via composition.
# Allow automation to prove the length requirement.
return conjunction.conclude_via_composition(automation=True)
return conjunction