Inference Rules: Difference between revisions
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imported>Desaperh Added rule REC_FUN_GOAL |
imported>Laurent Changed REC_FUN_GOAL to FUN_GOAL_REC and fixed typing. |
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{{RRRow}}|*||{{Rulename|TRUE_GOAL}}|| <math>\frac{}{\textbf{H} \;\;\vdash \;\; \btrue}</math> || || A | {{RRRow}}|*||{{Rulename|TRUE_GOAL}}|| <math>\frac{}{\textbf{H} \;\;\vdash \;\; \btrue}</math> || || A | ||
{{RRRow}}|*||{{Rulename|FUN_GOAL}}|| <math>\frac{}{\textbf{H},\; f\in | {{RRRow}}|*||{{Rulename|FUN_GOAL}}|| <math>\frac{}{\textbf{H},\; f\in E\;\mathit{op}\;F \;\;\vdash\;\; f\in T_1\pfun T_2}</math> || where <math>T_1</math> and <math>T_2</math> denote types and <math>\mathit{op}</math> is one of <math>\pfun</math>, <math>\tfun</math>, <math>\pinj</math>, <math>\tinj</math>, <math>\psur</math>, <math>\tsur</math>, <math>\tbij</math>. || A | ||
{{RRRow}}| ||{{Rulename| | {{RRRow}}| ||{{Rulename|FUN_GOAL_REC}}|| <math>\frac{}{\textbf{H},\; f\in S_1\;\mathit{op_1}\;(S_2\;\mathit{op_2}\;(\ldots(S_n\;\mathit{op_n}(U\;\mathit{opf}\;V\;))\ldots)) \;\vdash\;\; f(E_1)(E_2)...(E_n)\in T_1\pfun T_2}</math> || where <math>T_1</math> and <math>T_2</math> denote types, <math>\mathit{op}</math> denotes a set of relations (any arrow) and <math>\mathit{opf}</math> is one of <math>\pfun</math>, <math>\tfun</math>, <math>\pinj</math>, <math>\tinj</math>, <math>\psur</math>, <math>\tsur</math>, <math>\tbij</math>. || A | ||
{{RRRow}}|*||{{Rulename|DBL_HYP}}|| <math>\frac{\textbf{H},\;\textbf{P} \;\;\vdash \;\; \textbf{Q}}{\textbf{H},\;\textbf{P},\;\textbf{P} \;\;\vdash \;\; \textbf{Q}}</math> || || A | {{RRRow}}|*||{{Rulename|DBL_HYP}}|| <math>\frac{\textbf{H},\;\textbf{P} \;\;\vdash \;\; \textbf{Q}}{\textbf{H},\;\textbf{P},\;\textbf{P} \;\;\vdash \;\; \textbf{Q}}</math> || || A |
Revision as of 16:56, 25 August 2010
CAUTION! Any modification to this page shall be announced on the User mailing list!
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_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 |