Relation Rewrite Rules: Difference between revisions
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imported>Laurent Added rules SIMP_IN_FUNIMAGE*. |
imported>Laurent Removed SIMP_SPECIAL_LAMBDA (subsumed by SIMP_COMPSET_BFALSE) and generalized SIMP_DOM_LAMBDA and SIMP_RAN_LAMBDA. |
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{{RRRow}}|||{{Rulename|SIMP_RAN_PRJ1}}||<math> \ran (\prjone) \;\;\defi\;\; S </math>|| where <math>\prjone</math> has type <math>\pow(S \cprod T \cprod S)</math> || A | {{RRRow}}|||{{Rulename|SIMP_RAN_PRJ1}}||<math> \ran (\prjone) \;\;\defi\;\; S </math>|| where <math>\prjone</math> has type <math>\pow(S \cprod T \cprod S)</math> || A | ||
{{RRRow}}|||{{Rulename|SIMP_RAN_PRJ2}}||<math> \ran (\prjtwo) \;\;\defi\;\; T </math>|| where <math>\prjtwo</math> has type <math>\pow(S \cprod T \cprod T)</math> || A | {{RRRow}}|||{{Rulename|SIMP_RAN_PRJ2}}||<math> \ran (\prjtwo) \;\;\defi\;\; T </math>|| where <math>\prjtwo</math> has type <math>\pow(S \cprod T \cprod T)</math> || A | ||
{{RRRow}}|*||{{Rulename|SIMP_FUNIMAGE_LAMBDA}}||<math> (\lambda x \qdot P(x) \mid E(x))(y) \;\;\defi\;\; E(y) </math>|| || A | {{RRRow}}|*||{{Rulename|SIMP_FUNIMAGE_LAMBDA}}||<math> (\lambda x \qdot P(x) \mid E(x))(y) \;\;\defi\;\; E(y) </math>|| || A | ||
{{RRRow}}|||{{Rulename|SIMP_DOM_LAMBDA}}||<math> | {{RRRow}}|||{{Rulename|SIMP_DOM_LAMBDA}}||<math>\dom(\{x\qdot P\mid E\mapsto F) \;\;\defi\;\; \{x\qdot P\mid E\}</math>|| || A | ||
{{RRRow}}|||{{Rulename|SIMP_RAN_LAMBDA}}||<math> | {{RRRow}}|||{{Rulename|SIMP_RAN_LAMBDA}}||<math>\ran(\{x\qdot P\mid E\mapsto F) \;\;\defi\;\; \{x\qdot P\mid F\} </math>|| || A | ||
{{RRRow}}|||{{Rulename|SIMP_IN_FUNIMAGE}}||<math>E\mapsto F(E)\in F \;\;\defi\;\; \btrue</math>|| || A | {{RRRow}}|||{{Rulename|SIMP_IN_FUNIMAGE}}||<math>E\mapsto F(E)\in F \;\;\defi\;\; \btrue</math>|| || A | ||
{{RRRow}}|||{{Rulename|SIMP_IN_FUNIMAGE_CONVERSE_L}}||<math>F^{-1}(E)\mapsto E\in F \;\;\defi\;\; \btrue</math>|| || A | {{RRRow}}|||{{Rulename|SIMP_IN_FUNIMAGE_CONVERSE_L}}||<math>F^{-1}(E)\mapsto E\in F \;\;\defi\;\; \btrue</math>|| || A |
Revision as of 18:38, 6 December 2010
Rules that are marked with a * in the first column are implemented in the latest version of Rodin. Rules without a * are planned to be implemented in future versions. Other conventions used in these tables are described in The_Proving_Perspective_(Rodin_User_Manual)#Rewrite_Rules.
Name | Rule | Side Condition | A/M | |
---|---|---|---|---|
* | SIMP_DOM_COMPSET |
A | ||
SIMP_DOM_CONVERSE |
A | |||
* | SIMP_RAN_COMPSET |
A | ||
SIMP_RAN_CONVERSE |
A | |||
* | SIMP_SPECIAL_OVERL |
A | ||
SIMP_MULTI_OVERL |
there is a such that and and are syntactically equal. | A | ||
SIMP_TYPE_OVERL_CPROD |
where is a type expression | A | ||
SIMP_SPECIAL_DOMRES_L |
A | |||
SIMP_SPECIAL_DOMRES_R |
A | |||
SIMP_TYPE_DOMRES |
where is a type expression | A | ||
SIMP_MULTI_DOMRES_DOM |
A | |||
SIMP_MULTI_DOMRES_RAN |
A | |||
SIMP_DOMRES_ID |
A | |||
SIMP_SPECIAL_RANRES_R |
A | |||
SIMP_SPECIAL_RANRES_L |
A | |||
SIMP_TYPE_RANRES |
where is a type expression | A | ||
SIMP_MULTI_RANRES_RAN |
A | |||
SIMP_MULTI_RANRES_DOM |
A | |||
SIMP_RANRES_ID |
A | |||
SIMP_SPECIAL_DOMSUB_L |
A | |||
SIMP_SPECIAL_DOMSUB_R |
A | |||
SIMP_TYPE_DOMSUB |
where is a type expression | A | ||
SIMP_MULTI_DOMSUB_DOM |
A | |||
SIMP_DOMSUB_ID |
A | |||
SIMP_SPECIAL_RANSUB_R |
A | |||
SIMP_SPECIAL_RANSUB_L |
A | |||
SIMP_TYPE_RANSUB |
where is a type expression | A | ||
SIMP_MULTI_RANSUB_RAN |
A | |||
SIMP_RANSUB_ID |
A | |||
* | SIMP_SPECIAL_FCOMP |
A | ||
SIMP_TYPE_FCOMP_ID |
A | |||
SIMP_TYPE_FCOMP_R |
where is a type expression equal to | A | ||
SIMP_TYPE_FCOMP_L |
where is a type expression equal to | A | ||
SIMP_FCOMP_ID |
A | |||
* | SIMP_SPECIAL_BCOMP |
A | ||
SIMP_TYPE_BCOMP_ID |
A | |||
SIMP_TYPE_BCOMP_L |
where is a type expression equal to | A | ||
SIMP_TYPE_BCOMP_R |
where is a type expression equal to | A | ||
SIMP_BCOMP_ID |
A | |||
SIMP_SPECIAL_DPROD_R |
A | |||
SIMP_SPECIAL_DPROD_L |
A | |||
SIMP_DPROD_CPROD |
A | |||
SIMP_SPECIAL_PPROD_R |
A | |||
SIMP_SPECIAL_PPROD_L |
A | |||
SIMP_PPROD_CPROD |
A | |||
* | SIMP_SPECIAL_RELIMAGE_R |
A | ||
* | SIMP_SPECIAL_RELIMAGE_L |
A | ||
SIMP_TYPE_RELIMAGE |
where is a type expression | A | ||
SIMP_MULTI_RELIMAGE_DOM |
A | |||
SIMP_TYPE_RELIMAGE_ID |
A | |||
SIMP_RELIMAGE_ID |
A | |||
SIMP_MULTI_RELIMAGE_CPROD_SING |
where is a single expression | A | ||
SIMP_MULTI_RELIMAGE_SING_MAPSTO |
where is a single expression | A | ||
SIMP_MULTI_RELIMAGE_CONVERSE_RANSUB |
A | |||
SIMP_MULTI_RELIMAGE_CONVERSE_RANRES |
A | |||
SIMP_RELIMAGE_CONVERSE_DOMSUB |
A | |||
DERIV_RELIMAGE_RANSUB |
M | |||
DERIV_RELIMAGE_RANRES |
M | |||
SIMP_MULTI_RELIMAGE_DOMSUB |
A | |||
DERIV_RELIMAGE_DOMSUB |
M | |||
DERIV_RELIMAGE_DOMRES |
M | |||
SIMP_SPECIAL_CONVERSE |
A | |||
SIMP_CONVERSE_ID |
A | |||
SIMP_CONVERSE_CPROD |
A | |||
* | SIMP_CONVERSE_SETENUM |
A | ||
SIMP_CONVERSE_COMPSET |
A | |||
SIMP_DOM_ID |
where has type | A | ||
SIMP_RAN_ID |
where has type | A | ||
SIMP_FCOMP_ID_L |
A | |||
SIMP_FCOMP_ID_R |
A | |||
SIMP_SPECIAL_REL_R |
idem for operators | A | ||
SIMP_SPECIAL_REL_L |
idem for operators | A | ||
SIMP_SPECIAL_EQUAL_REL |
idem for operators | A | ||
SIMP_SPECIAL_EQUAL_RELDOM |
idem for operators | A | ||
SIMP_FUNIMAGE_PRJ1 |
A | |||
SIMP_FUNIMAGE_PRJ2 |
A | |||
SIMP_DOM_PRJ1 |
where has type | A | ||
SIMP_DOM_PRJ2 |
where has type | A | ||
SIMP_RAN_PRJ1 |
where has type | A | ||
SIMP_RAN_PRJ2 |
where has type | A | ||
* | SIMP_FUNIMAGE_LAMBDA |
A | ||
SIMP_DOM_LAMBDA |
A | |||
SIMP_RAN_LAMBDA |
A | |||
SIMP_IN_FUNIMAGE |
A | |||
SIMP_IN_FUNIMAGE_CONVERSE_L |
A | |||
SIMP_IN_FUNIMAGE_CONVERSE_R |
A | |||
SIMP_MULTI_FUNIMAGE_SETENUM_LL |
A | |||
SIMP_MULTI_FUNIMAGE_SETENUM_LR |
A | |||
* | SIMP_MULTI_FUNIMAGE_OVERL_SETENUM |
A | ||
SIMP_MULTI_FUNIMAGE_BUNION_SETENUM |
A | |||
* | SIMP_FUNIMAGE_CPROD |
A | ||
SIMP_FUNIMAGE_ID |
A | |||
* | SIMP_FUNIMAGE_FUNIMAGE_CONVERSE |
A | ||
* | SIMP_FUNIMAGE_CONVERSE_FUNIMAGE |
A | ||
* | SIMP_FUNIMAGE_FUNIMAGE_CONVERSE_SETENUM |
A | ||
* | SIMP_FUNIMAGE_DOMRES |
with hypothesis where is one of , , , , , , . | AM | |
* | SIMP_FUNIMAGE_DOMSUB |
with hypothesis where is one of , , , , , , . | AM | |
* | SIMP_FUNIMAGE_RANRES |
with hypothesis where is one of , , , , , , . | AM | |
* | SIMP_FUNIMAGE_RANSUB |
with hypothesis where is one of , , , , , , . | AM | |
* | SIMP_FUNIMAGE_SETMINUS |
with hypothesis where is one of , , , , , , . | AM | |
DEF_BCOMP |
M | |||
DERIV_ID_SING |
where is a single expression | M | ||
* | SIMP_SPECIAL_DOM |
A | ||
* | SIMP_SPECIAL_RAN |
A | ||
* | SIMP_CONVERSE_CONVERSE |
A | ||
* | DERIV_RELIMAGE_FCOMP |
M | ||
* | DERIV_FCOMP_DOMRES |
M | ||
* | DERIV_FCOMP_DOMSUB |
M | ||
* | DERIV_FCOMP_RANRES |
M | ||
* | DERIV_FCOMP_RANSUB |
M | ||
SIMP_SPECIAL_EQUAL_RELDOMRAN |
idem for operators | A | ||
SIMP_TYPE_DOM |
where is a type expression equal to | A | ||
SIMP_TYPE_RAN |
where is a type expression equal to | A | ||
SIMP_MULTI_DOM_CPROD |
A | |||
SIMP_MULTI_RAN_CPROD |
A | |||
* | DEF_IN_DOM |
M | ||
* | DEF_IN_RAN |
M | ||
* | DEF_IN_CONVERSE |
M | ||
* | DEF_IN_DOMRES |
M | ||
* | DEF_IN_RANRES |
M | ||
* | DEF_IN_DOMSUB |
M | ||
* | DEF_IN_RANSUB |
M | ||
* | DEF_IN_RELIMAGE |
M | ||
* | DEF_IN_FCOMP |
M | ||
* | DEF_OVERL |
M | ||
* | DEF_IN_ID |
M | ||
* | DEF_IN_DPROD |
M | ||
* | DEF_IN_PPROD |
M | ||
* | DEF_IN_REL |
M | ||
* | DEF_IN_RELDOM |
M | ||
* | DEF_IN_RELRAN |
M | ||
* | DEF_IN_RELDOMRAN |
M | ||
* | DEF_IN_FCT |
M | ||
* | DEF_IN_TFCT |
M | ||
* | DEF_IN_INJ |
M | ||
* | DEF_IN_TINJ |
M | ||
* | DEF_IN_SURJ |
M | ||
* | DEF_IN_TSURJ |
M | ||
* | DEF_IN_BIJ |
M | ||
DISTRI_BCOMP_BUNION |
M | |||
* | DISTRI_FCOMP_BUNION_R |
M | ||
* | DISTRI_FCOMP_BUNION_L |
M | ||
DISTRI_DPROD_BUNION |
M | |||
DISTRI_DPROD_BINTER |
M | |||
DISTRI_DPROD_SETMINUS |
M | |||
DISTRI_DPROD_OVERL |
M | |||
DISTRI_PPROD_BUNION |
M | |||
DISTRI_PPROD_BINTER |
M | |||
DISTRI_PPROD_SETMINUS |
M | |||
DISTRI_PPROD_OVERL |
M | |||
DISTRI_OVERL_BUNION_L |
M | |||
DISTRI_OVERL_BINTER_L |
M | |||
* | DISTRI_DOMRES_BUNION_R |
M | ||
* | DISTRI_DOMRES_BUNION_L |
M | ||
* | DISTRI_DOMRES_BINTER_R |
M | ||
* | DISTRI_DOMRES_BINTER_L |
M | ||
DISTRI_DOMRES_SETMINUS_R |
M | |||
DISTRI_DOMRES_SETMINUS_L |
M | |||
DISTRI_DOMRES_DPROD |
M | |||
DISTRI_DOMRES_OVERL |
M | |||
* | DISTRI_DOMSUB_BUNION_R |
M | ||
* | DISTRI_DOMSUB_BUNION_L |
M | ||
* | DISTRI_DOMSUB_BINTER_R |
M | ||
* | DISTRI_DOMSUB_BINTER_L |
M | ||
DISTRI_DOMSUB_DPROD |
M | |||
DISTRI_DOMSUB_OVERL |
M | |||
* | DISTRI_RANRES_BUNION_R |
M | ||
* | DISTRI_RANRES_BUNION_L |
M | ||
* | DISTRI_RANRES_BINTER_R |
M | ||
* | DISTRI_RANRES_BINTER_L |
M | ||
DISTRI_RANRES_SETMINUS_R |
M | |||
DISTRI_RANRES_SETMINUS_L |
M | |||
* | DISTRI_RANSUB_BUNION_R |
M | ||
* | DISTRI_RANSUB_BUNION_L |
M | ||
* | DISTRI_RANSUB_BINTER_R |
M | ||
* | DISTRI_RANSUB_BINTER_L |
M | ||
* | DISTRI_CONVERSE_BUNION |
M | ||
DISTRI_CONVERSE_BINTER |
M | |||
DISTRI_CONVERSE_SETMINUS |
M | |||
DISTRI_CONVERSE_BCOMP |
M | |||
DISTRI_CONVERSE_FCOMP |
M | |||
DISTRI_CONVERSE_PPROD |
M | |||
DISTRI_CONVERSE_DOMRES |
M | |||
DISTRI_CONVERSE_DOMSUB |
M | |||
DISTRI_CONVERSE_RANRES |
M | |||
DISTRI_CONVERSE_RANSUB |
M | |||
* | DISTRI_DOM_BUNION |
M | ||
* | DISTRI_RAN_BUNION |
M | ||
* | DISTRI_RELIMAGE_BUNION_R |
M | ||
* | DISTRI_RELIMAGE_BUNION_L |
M | ||
* | DERIV_DOM_TOTALREL |
with hypothesis , where is one of | M | |
DERIV_RAN_SURJREL |
with hypothesis , where is one of | M | ||
b | prjone-functional |
where is one of | A | |
b | prjtwo-functional |
where is one of | A | |
prj-expand |
M |