Definition df-inf 6984

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

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2		cB	. . 3 class B
3		cR	. . 3 class R
4	1, 2, 3	cinf 6982	. 2 class inf ( A , B , R )
5	3	ccnv 4626	. . 3 class `' R
6	1, 2, 5	csup 6981	. 2 class sup ( A , B , `' R )
7	4, 6	wceq 1353	1 wff inf ( A , B , R ) = sup ( A , B , `' R )

This definition is referenced by:  infeq1  7010  infeq2  7013  infeq3  7014  infeq123d  7015  nfinf  7016  eqinfti  7019  infvalti  7021  infclti  7022  inflbti  7023  infglbti  7024  infsnti  7029  inf00  7030  infisoti  7031  infex2g  7033  dfinfre  8913  infrenegsupex  9594  infxrnegsupex  11271