Inference Rules: Difference between revisions
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imported>Nicolas m Added comment for one point rule with 'exists' quantifier |
imported>Nicolas m added DIS_BINTER_L |
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{{RRRow}}|*||{{Rulename|OV_R}}|| <math>\frac{\textbf{H},\; G \in \dom(g) \;\;\vdash\;\;\textbf{Q}(g(G)) \qquad \textbf{H},\; \neg\, G \in \dom(g) \;\;\vdash\;\;\textbf{Q}(f(G))}{\textbf{H} \;\;\vdash \;\; \textbf{Q}((f\ovl g)(G)) \ \ \ \ \ }</math> || the <math>\ovl</math> operator must appear at the "top level" || M | {{RRRow}}|*||{{Rulename|OV_R}}|| <math>\frac{\textbf{H},\; G \in \dom(g) \;\;\vdash\;\;\textbf{Q}(g(G)) \qquad \textbf{H},\; \neg\, G \in \dom(g) \;\;\vdash\;\;\textbf{Q}(f(G))}{\textbf{H} \;\;\vdash \;\; \textbf{Q}((f\ovl g)(G)) \ \ \ \ \ }</math> || the <math>\ovl</math> operator must appear at the "top level" || M | ||
{{RRRow}}|*||{{Rulename|DIS_BINTER_R}}|| <math>\frac{\textbf{H} \;\;\vdash\;\; f^{-1} \in A \pfun B \qquad\textbf{H} \;\;\vdash\;\;\textbf{Q}(f[S] \binter f[T]) }{\textbf{H} \;\;\vdash \;\; \textbf{Q}(f[S \binter T]) \ \ \ \ \ }</math> || the occurrence of <math>f</math> must appear at the "top level". Moreover <math>A</math> and <math>B</math> denote some type. | {{RRRow}}|*||{{Rulename|DIS_BINTER_R}}|| <math>\frac{\textbf{H} \;\;\vdash\;\; f^{-1} \in A \pfun B \qquad\textbf{H} \;\;\vdash\;\;\textbf{Q}(f[S] \binter f[T]) }{\textbf{H} \;\;\vdash \;\; \textbf{Q}(f[S \binter T]) \ \ \ \ \ }</math> || the occurrence of <math>f</math> must appear at the "top level". Moreover <math>A</math> and <math>B</math> denote some type. || M | ||
{{RRRow}}|*||{{Rulename|DIS_BINTER_L}}|| <math>\frac{\textbf{H} \;\;\vdash\;\; f^{-1} \in A \pfun B \qquad\textbf{H},\;\textbf{Q}(f[S] \binter f[T]) \;\;\vdash\;\;\textbf{G}}{\textbf{H},\; \textbf{Q}(f[S \binter T]) \;\;\vdash \;\; \textbf{G} \ \ \ \ \ }</math> || the occurrence of <math>f</math> must appear at the "top level". Moreover <math>A</math> and <math>B</math> denote some type. || M | |||
{{RRRow}}|*||{{Rulename|DIS_SETMINUS_R}}|| <math>\frac{\textbf{H} \;\;\vdash\;\; f^{-1} \in A \pfun B \qquad\textbf{H} \;\;\vdash\;\;\textbf{Q}(f[S] \setminus f[T]) }{\textbf{H} \;\;\vdash \;\; \textbf{Q}(f[S \setminus T]) \ \ \ \ \ }</math> || the occurrence of <math>f</math> must appear at the "top level". Moreover <math>A</math> and <math>B</math> denote some type. Similar left distribution rules exist || M | {{RRRow}}|*||{{Rulename|DIS_SETMINUS_R}}|| <math>\frac{\textbf{H} \;\;\vdash\;\; f^{-1} \in A \pfun B \qquad\textbf{H} \;\;\vdash\;\;\textbf{Q}(f[S] \setminus f[T]) }{\textbf{H} \;\;\vdash \;\; \textbf{Q}(f[S \setminus T]) \ \ \ \ \ }</math> || the occurrence of <math>f</math> must appear at the "top level". Moreover <math>A</math> and <math>B</math> denote some type. Similar left distribution rules exist || M |
Revision as of 13:20, 17 August 2009
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
| |
* | 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
| ||
* | CONTRADICT_L |
M
| ||
* | CONTRADICT_R |
M
| ||
* | CASE |
M
| ||
* | MH |
M
| ||
* | HM |
M
| ||
* | EQV |
M
| ||
* | OV_L |
the operator must appear at the "top level" | M
| |
* | OV_R |
the operator must appear at the "top level" | M
| |
* | OV_L |
the operator must appear at the "top level" | M
| |
* | OV_R |
the operator must appear at the "top level" | M
| |
* | 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. Similar left distribution rules exist | M
| |
* | SIM_REL_IMAGE_R |
the occurrence of must appear at the "top level". A similar left simplification rule exists. | M
| |
* | SIM_FCOMP_R |
the occurrence of must appear at the "top level". A similar left simplification rule exists. | 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 |
the user has to write the set corresponding to in the editing area of the Proof Control Window | M
| |
* | FIN_REL_RAN_R |
the user has to write the set corresponding to in the editing area of the Proof Control Window | M
| |
* | FIN_REL_DOM_R |
the user has to write the set corresponding to in the editing area of the Proof Control Window | 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
| |
* | CARD_SUBSETEQ |
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 |