:: RCOMP_2 semantic presentation
theorem :: RCOMP_2:1
canceled;
theorem :: RCOMP_2:2
:: deftheorem defines [. RCOMP_2:def 1 :
:: deftheorem defines ]. RCOMP_2:def 2 :
theorem :: RCOMP_2:3
theorem :: RCOMP_2:4
theorem :: RCOMP_2:5
theorem :: RCOMP_2:6
theorem :: RCOMP_2:7
theorem :: RCOMP_2:8
theorem :: RCOMP_2:9
theorem :: RCOMP_2:10
theorem :: RCOMP_2:11
theorem :: RCOMP_2:12
theorem :: RCOMP_2:13
theorem :: RCOMP_2:14
theorem :: RCOMP_2:15
theorem :: RCOMP_2:16
theorem :: RCOMP_2:17
for
p,
q being
real number holds
(
].p,q.[ c= [.p,q.[ &
].p,q.[ c= ].p,q.] &
[.p,q.[ c= [.p,q.] &
].p,q.] c= [.p,q.] )
by XXREAL_1:21, XXREAL_1:22, XXREAL_1:23, XXREAL_1:24;
theorem :: RCOMP_2:18
theorem :: RCOMP_2:19
theorem :: RCOMP_2:20
theorem :: RCOMP_2:21
theorem :: RCOMP_2:22
theorem :: RCOMP_2:23
theorem :: RCOMP_2:24
for
q1,
q2,
p1,
p2 being
real number st
[.q1,q2.[ meets [.p1,p2.[ holds
[.q1,q2.[ \/ [.p1,p2.[ = [.(min q1,p1),(max q2,p2).[ by XXREAL_1:162;
theorem :: RCOMP_2:25
for
q1,
q2,
p1,
p2 being
real number st
].q1,q2.] meets ].p1,p2.] holds
].q1,q2.] \/ ].p1,p2.] = ].(min q1,p1),(max q2,p2).] by XXREAL_1:164;
theorem :: RCOMP_2:26
theorem :: RCOMP_2:27