Inference Rules: Difference between revisions
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imported>Laurent m Rules MH and HM have been fixed |
imported>Tommy m removed * on unimplemented rules |
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{{RRRow}}|*||{{Rulename|AND_R}}|| <math>\frac{\textbf{H} \; \; \vdash \; \; \textbf{P} \qquad \textbf{H} \; \; \vdash \; \; \textbf{Q}}{\textbf{H} \; \; \vdash \; \; \textbf{P} \; \land \; \textbf{Q}}</math> || || A | {{RRRow}}|*||{{Rulename|AND_R}}|| <math>\frac{\textbf{H} \; \; \vdash \; \; \textbf{P} \qquad \textbf{H} \; \; \vdash \; \; \textbf{Q}}{\textbf{H} \; \; \vdash \; \; \textbf{P} \; \land \; \textbf{Q}}</math> || || A | ||
{{RRRow}}| | {{RRRow}}|||{{Rulename|IMP_L1}}|| <math>\frac{\textbf{H},\; \textbf{Q},\; \textbf{P} \land \ldots \land \textbf{R} \limp \textbf{S} \;\;\vdash \;\; \textbf{T}}{\textbf{H},\; \textbf{Q},\; \textbf{P} \land \ldots \land \textbf{Q} \land \ldots \land \textbf{R} \limp \textbf{S} \;\;\vdash \;\; \textbf{T} }</math> || || A | ||
{{RRRow}}|*||{{Rulename|IMP_R}}|| <math>\frac{\textbf{H}, \textbf{P} \;\;\vdash \;\; \textbf{Q}}{\textbf{H} \;\;\vdash \;\; \textbf{P} \limp \textbf{Q}}</math> || || A | {{RRRow}}|*||{{Rulename|IMP_R}}|| <math>\frac{\textbf{H}, \textbf{P} \;\;\vdash \;\; \textbf{Q}}{\textbf{H} \;\;\vdash \;\; \textbf{P} \limp \textbf{Q}}</math> || || A | ||
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{{RRRow}}|*||{{Rulename|HM}}|| <math>\frac{\textbf{H} \;\;\vdash\;\;\neg\,\textbf{Q} \qquad \textbf{H},\; \neg\,\textbf{P} \;\;\vdash \;\; \textbf{R} }{\textbf{H},\;\textbf{P} \limp \textbf{Q} \;\;\vdash \;\; \textbf{R}}</math> || || M | {{RRRow}}|*||{{Rulename|HM}}|| <math>\frac{\textbf{H} \;\;\vdash\;\;\neg\,\textbf{Q} \qquad \textbf{H},\; \neg\,\textbf{P} \;\;\vdash \;\; \textbf{R} }{\textbf{H},\;\textbf{P} \limp \textbf{Q} \;\;\vdash \;\; \textbf{R}}</math> || || M | ||
{{RRRow}}| | {{RRRow}}|||{{Rulename|EQV}}|| <math>\frac{\textbf{H(Q)},\; \textbf{P} \leqv \textbf{Q} | ||
\;\;\vdash\;\; \textbf{G(Q)}}{\textbf{H(P)},\;\textbf{P} \leqv \textbf{Q} | \;\;\vdash\;\; \textbf{G(Q)}}{\textbf{H(P)},\;\textbf{P} \leqv \textbf{Q} | ||
\;\;\vdash \;\; \textbf{G(P)}}</math> || || M | \;\;\vdash \;\; \textbf{G(P)}}</math> || || M | ||
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{{RRRow}}|*||{{Rulename|FIN_GE_0}}|| <math>\frac{\textbf{H} \;\;\vdash \;\; \exists n\,\qdot\, (\forall x \,\qdot\, x \in S \;\limp\; x \leq n) \qquad \textbf{H} \;\;\vdash \;\; S \subseteq \nat }{\textbf{H} \;\;\vdash \;\; \finite(S)}</math> || || M | {{RRRow}}|*||{{Rulename|FIN_GE_0}}|| <math>\frac{\textbf{H} \;\;\vdash \;\; \exists n\,\qdot\, (\forall x \,\qdot\, x \in S \;\limp\; x \leq n) \qquad \textbf{H} \;\;\vdash \;\; S \subseteq \nat }{\textbf{H} \;\;\vdash \;\; \finite(S)}</math> || || M | ||
{{RRRow}}| | {{RRRow}}|||{{Rulename|CARD_INTERV}}|| <math>\frac{\textbf{H},\, a \leq b \;\;\vdash \;\; \textbf{Q}(b-a+1) \qquad \textbf{H},\, b < a \;\;\vdash \;\; \textbf{Q}(0) }{\textbf{H} \;\;\vdash\;\; \textbf{Q}(\card\,(a\upto b))}</math> || <math>\card (a \upto b)</math> must appear at "top-level" || M | ||
{{RRRow}}|b||{{Rulename|CARD_EMPTY_INTERV}}|| <math>\frac{\textbf{H},\, a \leq b,\,\textbf{P}(b-a+1) \;\;\vdash \;\; \textbf{Q} \qquad \textbf{H},\, b < a ,\, \textbf{P}(0)\;\;\vdash \;\; \textbf{Q} }{\textbf{H},\,\textbf{P}(\card\,(a\upto b)) \;\;\vdash\;\; \textbf{Q}}</math> || <math>\card (a \upto b)</math> must appear at "top-level" || M | {{RRRow}}|b||{{Rulename|CARD_EMPTY_INTERV}}|| <math>\frac{\textbf{H},\, a \leq b,\,\textbf{P}(b-a+1) \;\;\vdash \;\; \textbf{Q} \qquad \textbf{H},\, b < a ,\, \textbf{P}(0)\;\;\vdash \;\; \textbf{Q} }{\textbf{H},\,\textbf{P}(\card\,(a\upto b)) \;\;\vdash\;\; \textbf{Q}}</math> || <math>\card (a \upto b)</math> must appear at "top-level" || M |
Revision as of 09:25, 21 December 2009
Conventions used in these tables are described in The_Proving_Perspective_(Rodin_User_Manual)#Inference_Rules.
Rules that are marked with a b in the first column are currently broken in Rodin 1.1 (see bug 2895507).
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
| ||
* | 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_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. | 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
| |
b | 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
| ||
b | 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
| ||
b | FIN_FUN1_R |
the user has to write the set corresponding to in the editing area of the Proof Control Window | M
| |
b | FIN_FUN2_R |
the user has to write the set corresponding to in the editing area of the Proof Control Window | M
| |
b | FIN_FUN_IMG_R |
the user has to write the set corresponding to in the editing area of the Proof Control Window | M
| |
b | FIN_FUN_RAN_R |
the user has to write the set corresponding to in the editing area of the Proof Control Window | M
| |
b | 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
| ||
b | CARD_EMPTY_INTERV |
must appear at "top-level" | M
| |
b | CARD_SUBSETEQ |
and bear the same type | 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
| |
b | 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 |