## File: theorems.tex

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hol88 2.02.19940316-35
 `1234567891011121314151617181920212223242526272829` ``````\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 ``````