Definition df-pi 13350

Description: Define pi = 3.14159..., which is the smallest positive number whose sine is zero. Definition of pi in [Gleason] p. 311. (We use the inverse of less-than, " `' <", to turn supremum into infimum; currently we don't have infimum defined separately.) (Contributed by Paul Chapman, 23-Jan-2008.)

Assertion

Ref	Expression
df-pi	|- pi = sup ( ( RR+ i^i ( `' sin " { 0 } ) ) , RR , `' < )

Detailed syntax breakdown of Definition df-pi

Step	Hyp	Ref	Expression
1		cpi 13344	. 2 class pi
2		crp 10983	. . . 4 class RR+
3		csin 13341	. . . . . 6 class sin
4	3	ccnv 4834	. . . . 5 class `' sin
5		cc0 9274	. . . . . 6 class 0
6	5	csn 3872	. . . . 5 class { 0 }
7	4, 6	cima 4838	. . . 4 class ( `' sin " { 0 } )
8	2, 7	cin 3322	. . 3 class ( RR+ i^i ( `' sin " { 0 } ) )
9		cr 9273	. . 3 class RR
10		clt 9410	. . . 4 class <
11	10	ccnv 4834	. . 3 class `' <
12	8, 9, 11	csup 7682	. 2 class sup ( ( RR+ i^i ( `' sin " { 0 } ) ) , RR , `' < )
13	1, 12	wceq 1369	1 wff pi = sup ( ( RR+ i^i ( `' sin " { 0 } ) ) , RR , `' < )

This definition is referenced by:  pilem2  21897  pilem3  21898