Inference Rules: Difference between revisions
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imported>Laurent Rule FUN_IMAGE_GOAL is manual |
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<font color=red>CAUTION! Any modification to this page shall be announced on the [[#Mailing_lists |User]] mailing list!</font> | <font color=red>CAUTION! Any modification to this page shall be announced on the [[#Mailing_lists |User]] mailing list!</font> | ||
Rules that are marked with a <tt>*</tt> in the first column are implemented in the latest version of Rodin. | |||
Rules without a <tt>*</tt> are planned to be implemented in future versions. | |||
Other conventions used in these tables are described in [[The_Proving_Perspective_%28Rodin_User_Manual%29#Inference_Rules]]. | |||
<!-- | <!-- | ||
Rules that are marked with a <tt>b</tt> in the first column are currently broken in Rodin 1.1 (see [http://sourceforge.net/tracker/?func=detail&aid=2895507&group_id=108850&atid=651669 bug 2895507]). | Rules that are marked with a <tt>b</tt> in the first column are currently broken in Rodin 1.1 (see [http://sourceforge.net/tracker/?func=detail&aid=2895507&group_id=108850&atid=651669 bug 2895507]). |
Revision as of 12:14, 30 August 2010
CAUTION! Any modification to this page shall be announced on the User mailing list!
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)#Inference_Rules.
Name | Rule | Side Condition | A/M
| |
---|---|---|---|---|
* | HYP |
A
| ||
* | HYP_OR |
A
| ||
* | CNTR |
A
| ||
* | FALSE_HYP |
A
| ||
* | TRUE_GOAL |
A
| ||
* | FUN_GOAL |
where and denote types and is one of , , , , , , . | A
| |
FUN_IMAGE_GOAL |
where denotes a set of relations (any arrow) and occurs at the top level | M
| ||
FUN_GOAL_REC |
where and denote types, denotes a set of relations (any arrow) and is one of , , , , , , . | A
| ||
* | DBL_HYP |
A
| ||
* | AND_L |
A
| ||
* | AND_R |
A
| ||
IMP_L1 |
A
| |||
* | IMP_R |
A
| ||
* | IMP_AND_L |
A
| ||
* | IMP_OR_L |
A
| ||
* | AUTO_MH |
A
| ||
* | NEG_IN_L |
A
| ||
* | NEG_IN_R |
A
| ||
* | XST_L |
A
| ||
* | ALL_R |
A
| ||
* | EQL_LR |
is a variable which is not free in | A
| |
* | EQL_RL |
is a variable which is not free in | A
| |
SUBSET_INTER |
the operator must appear at the "top level" | A
| ||
IN_INTER |
the operator must appear at the "top level" | A
| ||
NOTIN_INTER |
the operator must appear at the "top level" | A
| ||
* | FIN_L_LOWER_BOUND_L |
The goal is discharged | A
| |
* | FIN_L_LOWER_BOUND_R |
The goal is discharged | A
| |
* | FIN_L_UPPER_BOUND_L |
The goal is discharged | A
| |
* | FIN_L_UPPER_BOUND_R |
The goal is discharged | A
| |
* | CONTRADICT_L |
M
| ||
* | CONTRADICT_R |
M
| ||
* | CASE |
M
| ||
* | MH |
M
| ||
* | HM |
M
| ||
EQV |
M
| |||
* | OV_SETENUM_L |
the operator must appear at the "top level" | A
| |
* | OV_SETENUM_R |
the operator must appear at the "top level" | A
| |
* | OV_L |
the operator must appear at the "top level" | A
| |
* | OV_R |
the operator must appear at the "top level" | A
| |
* | DIS_BINTER_R |
the occurrence of must appear at the "top level". Moreover and denote some type. | M
| |
* | DIS_BINTER_L |
the occurrence of must appear at the "top level". Moreover and denote some type. | M
| |
* | DIS_SETMINUS_R |
the occurrence of must appear at the "top level". Moreover and denote some type. | M
| |
* | DIS_SETMINUS_L |
the occurrence of must appear at the "top level". Moreover and denote some type. | M
| |
* | SIM_REL_IMAGE_R |
the occurrence of must appear at the "top level". | M
| |
* | SIM_REL_IMAGE_L |
the occurrence of must appear at the "top level". | M
| |
* | SIM_FCOMP_R |
the occurrence of must appear at the "top level". | M
| |
* | SIM_FCOMP_L |
the occurrence of must appear at the "top level". | M
| |
* | FIN_SUBSETEQ_R |
the user has to write the set corresponding to in the editing area of the Proof Control Window | M
| |
* | FIN_BINTER_R |
M
| ||
* | FIN_SETMINUS_R |
M
| ||
* | FIN_REL_R |
the user has to write the set corresponding to in the editing area of the Proof Control Window | M
| |
* | FIN_REL_IMG_R |
M
| ||
* | FIN_REL_RAN_R |
M
| ||
* | FIN_REL_DOM_R |
M
| ||
* | FIN_FUN1_R |
the user has to write the set corresponding to in the editing area of the Proof Control Window | M
| |
* | FIN_FUN2_R |
the user has to write the set corresponding to in the editing area of the Proof Control Window | M
| |
* | FIN_FUN_IMG_R |
the user has to write the set corresponding to in the editing area of the Proof Control Window | M
| |
* | FIN_FUN_RAN_R |
the user has to write the set corresponding to in the editing area of the Proof Control Window | M
| |
* | FIN_FUN_DOM_R |
the user has to write the set corresponding to in the editing area of the Proof Control Window | M
| |
* | LOWER_BOUND_L |
must not contain any bound variable | M
| |
* | LOWER_BOUND_R |
must not contain any bound variable | M
| |
* | UPPER_BOUND_L |
must not contain any bound variable | M
| |
* | UPPER_BOUND_R |
must not contain any bound variable | M
| |
* | FIN_LT_0 |
M
| ||
* | FIN_GE_0 |
M
| ||
CARD_INTERV |
must appear at "top-level" | M
| ||
CARD_EMPTY_INTERV |
must appear at "top-level" | M
| ||
* | DERIV_LE_CARD |
and bear the same type | M
| |
* | DERIV_GE_CARD |
and bear the same type | M
| |
* | DERIV_LT_CARD |
and bear the same type | M
| |
* | DERIV_GT_CARD |
and bear the same type | M
| |
* | DERIV_EQUAL_CARD |
and bear the same type | M
| |
SIMP_CARD_SETMINUS_L |
must appear at "top-level" | M | ||
SIMP_CARD_SETMINUS_R |
must appear at "top-level" | M
| ||
SIMP_CARD_CPROD_L |
must appear at "top-level" | M | ||
SIMP_CARD_CPROD_R |
must appear at "top-level" | M
| ||
* | FORALL_INST |
is instantiated with | M
| |
* | FORALL_INST_MP |
is instantiated with and a Modus Ponens is applied | M
| |
* | CUT |
hypothesis is added | M
| |
* | EXISTS_INST |
is instantiated with | M
| |
* | DISTINCT_CASE |
case distinction on predicate | M
| |
ONE_POINT_L |
The rule can be applied with as well as with | A
| ||
ONE_POINT_R |
The rule can be applied with as well as with | A
| ||
DATATYPE_DISTINCT_CASE |
where has a datatype as type and appears free in , has constructors , parameters are introduced as fresh identifiers | M
| ||
DATATYPE_INDUCTION |
(N = Non inductive; I = Inductive) where has inductive datatype as type and appears free in ; are constructors of ; an antecedent is created for each and each , an hypothesis is added for each ; all parameters are introduced as fresh identifiers | M |