:: GOBRD11 semantic presentation
Lemma36:
sqrt 2 > 0
by SQUARE_1:93;
theorem Th1: :: GOBRD11:1
theorem Th2: :: GOBRD11:2
theorem Th3: :: GOBRD11:3
theorem Th4: :: GOBRD11:4
theorem Th5: :: GOBRD11:5
theorem Th6: :: GOBRD11:6
Lemma58:
the carrier of (TOP-REAL 2) = REAL 2
by EUCLID:25;
theorem Th7: :: GOBRD11:7
Lemma107:
for s1 being Real holds { |[tb,sb]| where tb is Real, sb is Real : sb >= s1 } is Subset of (TOP-REAL 2)
Lemma111:
for s1 being Real holds { |[tb,sb]| where tb is Real, sb is Real : sb > s1 } is Subset of (TOP-REAL 2)
Lemma112:
for s1 being Real holds { |[tb,sb]| where tb is Real, sb is Real : sb <= s1 } is Subset of (TOP-REAL 2)
Lemma113:
for s1 being Real holds { |[tb,sb]| where tb is Real, sb is Real : sb < s1 } is Subset of (TOP-REAL 2)
Lemma114:
for s1 being Real holds { |[sb,tb]| where sb is Real, tb is Real : sb <= s1 } is Subset of (TOP-REAL 2)
Lemma115:
for s1 being Real holds { |[sb,tb]| where sb is Real, tb is Real : sb < s1 } is Subset of (TOP-REAL 2)
Lemma116:
for s1 being Real holds { |[sb,tb]| where sb is Real, tb is Real : sb >= s1 } is Subset of (TOP-REAL 2)
Lemma117:
for s1 being Real holds { |[sb,tb]| where sb is Real, tb is Real : sb > s1 } is Subset of (TOP-REAL 2)
theorem Th8: :: GOBRD11:8
theorem Th9: :: GOBRD11:9
theorem Th10: :: GOBRD11:10
theorem Th11: :: GOBRD11:11
theorem Th12: :: GOBRD11:12
theorem Th13: :: GOBRD11:13
theorem Th14: :: GOBRD11:14
theorem Th15: :: GOBRD11:15
theorem Th16: :: GOBRD11:16
theorem Th17: :: GOBRD11:17
theorem Th18: :: GOBRD11:18
theorem Th19: :: GOBRD11:19
theorem Th20: :: GOBRD11:20
theorem Th21: :: GOBRD11:21
theorem Th22: :: GOBRD11:22
theorem Th23: :: GOBRD11:23
theorem Th24: :: GOBRD11:24
theorem Th25: :: GOBRD11:25
theorem Th26: :: GOBRD11:26
theorem Th27: :: GOBRD11:27
theorem Th28: :: GOBRD11:28
theorem Th29: :: GOBRD11:29
theorem Th30: :: GOBRD11:30
theorem Th31: :: GOBRD11:31
theorem Th32: :: GOBRD11:32
theorem Th33: :: GOBRD11:33
theorem Th34: :: GOBRD11:34
theorem Th35: :: GOBRD11:35