:: Some Topological Properties of Cells in $R^2$
:: by Yatsuka Nakamura and Andrzej Trybulec
::
:: Received July 22, 1996
:: Copyright (c) 1996 Association of Mizar Users
Lm1:
sqrt 2 > 0
by SQUARE_1:93;
theorem Th1: :: GOBRD11:1
theorem :: GOBRD11:2
theorem :: GOBRD11:3
theorem :: GOBRD11:4
theorem :: GOBRD11:5
theorem Th6: :: GOBRD11:6
Lm2:
the carrier of (TOP-REAL 2) = REAL 2
by EUCLID:25;
theorem :: GOBRD11:7
Lm3:
for s1 being Real holds { |[tb,sb]| where tb, sb is Real : sb >= s1 } is Subset of (TOP-REAL 2)
Lm4:
for s1 being Real holds { |[tb,sb]| where tb, sb is Real : sb > s1 } is Subset of (TOP-REAL 2)
Lm5:
for s1 being Real holds { |[tb,sb]| where tb, sb is Real : sb <= s1 } is Subset of (TOP-REAL 2)
Lm6:
for s1 being Real holds { |[tb,sb]| where tb, sb is Real : sb < s1 } is Subset of (TOP-REAL 2)
Lm7:
for s1 being Real holds { |[sb,tb]| where sb, tb is Real : sb <= s1 } is Subset of (TOP-REAL 2)
Lm8:
for s1 being Real holds { |[sb,tb]| where sb, tb is Real : sb < s1 } is Subset of (TOP-REAL 2)
Lm9:
for s1 being Real holds { |[sb,tb]| where sb, tb is Real : sb >= s1 } is Subset of (TOP-REAL 2)
Lm10:
for s1 being Real holds { |[sb,tb]| where sb, 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 :: GOBRD11:35