File: theorems.tex

package info (click to toggle)
hol88 2.02.19940316-35
  • links: PTS
  • area: main
  • in suites: bullseye, buster, sid
  • size: 65,988 kB
  • ctags: 21,623
  • sloc: ml: 199,939; ansic: 9,666; sh: 7,118; makefile: 6,095; lisp: 2,747; yacc: 894; sed: 201; cpp: 87; awk: 5
file content (29 lines) | stat: -rw-r--r-- 1,078 bytes parent folder | download | duplicates (5)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
\chapter{Pre-proved Theorems}\input{theorems-intro}\THEOREM DISJ\_RESQ\_EXISTS\_DIST res\_quan
|- !P Q R.
   (?i :: \i. P i \/ Q i. R i) = (?i :: P. R i) \/ (?i :: Q. R i)
\ENDTHEOREM
\THEOREM RESQ\_EXISTS\_DISJ\_DIST res\_quan
|- !P Q R. (?i :: P. Q i \/ R i) = (?i :: P. Q i) \/ (?i :: P. R i)
\ENDTHEOREM
\THEOREM RESQ\_EXISTS\_REORDER res\_quan
|- !P Q R. (?i :: P. ?j :: Q. R i j) = (?j :: Q. ?i :: P. R i j)
\ENDTHEOREM
\THEOREM RESQ\_EXISTS\_UNIQUE res\_quan
|- !P j. (?i :: $= j. P i) = P j
\ENDTHEOREM
\THEOREM RESQ\_FORALL\_CONJ\_DIST res\_quan
|- !P Q R. (!i :: P. Q i /\ R i) = (!i :: P. Q i) /\ (!i :: P. R i)
\ENDTHEOREM
\THEOREM RESQ\_FORALL\_DISJ\_DIST res\_quan
|- !P Q R.
   (!i :: \i. P i \/ Q i. R i) = (!i :: P. R i) /\ (!i :: Q. R i)
\ENDTHEOREM
\THEOREM RESQ\_FORALL\_FORALL res\_quan
|- !P R x. (!x. !i :: P. R i x) = (!i :: P. !x. R i x)
\ENDTHEOREM
\THEOREM RESQ\_FORALL\_REORDER res\_quan
|- !P Q R. (!i :: P. !j :: Q. R i j) = (!j :: Q. !i :: P. R i j)
\ENDTHEOREM
\THEOREM RESQ\_FORALL\_UNIQUE res\_quan
|- !P j. (!i :: $= j. P i) = P j
\ENDTHEOREM