:: REWRITE2 semantic presentation
theorem ThSeq10: :: REWRITE2:1
theorem ThSeq40: :: REWRITE2:2
theorem ThRed9: :: REWRITE2:3
theorem ThRed10: :: REWRITE2:4
:: deftheorem defXFin defines XFinSequence-yielding REWRITE2:def 1 :
:: deftheorem defConcatL defines ^+ REWRITE2:def 2 :
:: deftheorem defConcatR defines +^ REWRITE2:def 3 :
theorem ThConcatLen: :: REWRITE2:5
theorem :: REWRITE2:6
theorem :: REWRITE2:7
theorem :: REWRITE2:8
theorem :: REWRITE2:9
:: deftheorem defProd defines -->. REWRITE2:def 4 :
:: deftheorem defDeriv1 defines ==>. REWRITE2:def 5 :
theorem ThProd10: :: REWRITE2:10
theorem :: REWRITE2:11
theorem ThProd30: :: REWRITE2:12
theorem ThProd40: :: REWRITE2:13
theorem ThProd50: :: REWRITE2:14
theorem ThProd60: :: REWRITE2:15
theorem ThProd70: :: REWRITE2:16
theorem ThProd80: :: REWRITE2:17
theorem ThProd90: :: REWRITE2:18
theorem ThProd100: :: REWRITE2:19
theorem ThProd110: :: REWRITE2:20
theorem ThProd120: :: REWRITE2:21
definition
let E be
set ;
let S be
semi-Thue-system of
E;
func ==>.-relation S -> Relation of
E ^omega means :
defRed:
:: REWRITE2:def 6
for
s,
t being
Element of
E ^omega holds
(
[s,t] in it iff
s ==>. t,
S );
existence
ex b1 being Relation of E ^omega st
for s, t being Element of E ^omega holds
( [s,t] in b1 iff s ==>. t,S )
uniqueness
for b1, b2 being Relation of E ^omega st ( for s, t being Element of E ^omega holds
( [s,t] in b1 iff s ==>. t,S ) ) & ( for s, t being Element of E ^omega holds
( [s,t] in b2 iff s ==>. t,S ) ) holds
b1 = b2
end;
:: deftheorem defRed defines ==>.-relation REWRITE2:def 6 :
theorem ThRedSeq5: :: REWRITE2:22
theorem ThRedSeq10: :: REWRITE2:23
theorem :: REWRITE2:24
theorem ThRedSeq30: :: REWRITE2:25
theorem ThRedSeq40: :: REWRITE2:26
theorem ThRedSeq45: :: REWRITE2:27
theorem ThRedSeq50: :: REWRITE2:28
theorem ThRedSeq60: :: REWRITE2:29
theorem ThRedSeq69: :: REWRITE2:30
theorem ThRedSeq70: :: REWRITE2:31
:: deftheorem defDerivN defines ==>* REWRITE2:def 7 :
theorem ThDerivN10: :: REWRITE2:32
theorem ThDerivN20: :: REWRITE2:33
theorem :: REWRITE2:34
theorem ThDerivN40: :: REWRITE2:35
theorem ThDerivN50: :: REWRITE2:36
theorem ThDerivN60: :: REWRITE2:37
theorem :: REWRITE2:38
theorem :: REWRITE2:39
theorem ThDerivN80: :: REWRITE2:40
theorem ThDerivN90: :: REWRITE2:41
theorem ThDerivN100: :: REWRITE2:42
theorem ThDerivN110: :: REWRITE2:43
theorem ThDerivN119: :: REWRITE2:44
theorem ThDerivN120: :: REWRITE2:45
:: deftheorem defines Lang REWRITE2:def 8 :
theorem ThLang10: :: REWRITE2:46
theorem ThLang15: :: REWRITE2:47
theorem ThLang20: :: REWRITE2:48
theorem ThLang25: :: REWRITE2:49
theorem ThLang29: :: REWRITE2:50
theorem :: REWRITE2:51
:: deftheorem defEq defines are_equivalent_wrt REWRITE2:def 9 :
theorem :: REWRITE2:52
theorem :: REWRITE2:53
theorem :: REWRITE2:54
theorem :: REWRITE2:55
theorem ThEq50: :: REWRITE2:56
theorem ThEq60: :: REWRITE2:57
theorem ThEq68: :: REWRITE2:58
theorem ThEq69: :: REWRITE2:59
theorem ThEq70: :: REWRITE2:60
theorem :: REWRITE2:61
theorem :: REWRITE2:62