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Definition df-inf 6601
Description: Define the infimum of class  A. It is meaningful when  R is a relation that strictly orders 
B and when the infimum exists. For example,  R could be 'less than',  B could be the set of real numbers, and  A could be the set of all positive reals; in this case the infimum is 0. The infimum is defined as the supremum using the converse ordering relation. In the given example, 0 is the supremum of all reals (greatest real number) for which all positive reals are greater. (Contributed by AV, 2-Sep-2020.)
Assertion
Ref Expression
df-inf  |- inf ( A ,  B ,  R
)  =  sup ( A ,  B ,  `' R )

Detailed syntax breakdown of Definition df-inf
StepHypRef Expression
1 cA . . 3  class  A
2 cB . . 3  class  B
3 cR . . 3  class  R
41, 2, 3cinf 6599 . 2  class inf ( A ,  B ,  R
)
53ccnv 4403 . . 3  class  `' R
61, 2, 5csup 6598 . 2  class  sup ( A ,  B ,  `' R )
74, 6wceq 1287 1  wff inf ( A ,  B ,  R
)  =  sup ( A ,  B ,  `' R )
Colors of variables: wff set class
This definition is referenced by:  infeq1  6627  infeq2  6630  infeq3  6631  infeq123d  6632  nfinf  6633  eqinfti  6636  infvalti  6638  infclti  6639  inflbti  6640  infglbti  6641  infsnti  6646  inf00  6647  infisoti  6648  dfinfre  8329  infrenegsupex  8991
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