Arithmetic Rewrite Rules
From Event-B
Revision as of 14:00, 8 December 2010 by imported>Benoit (Renamed SIMP_CARD_ID in SIMP_CARD_ID_DOMRES and added SIMP_CARD_ID)
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_SPECIAL_MOD_0 |
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A | ||
SIMP_SPECIAL_MOD_1 |
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A | ||
SIMP_MIN_SING |
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where ![]() |
A | |
SIMP_MAX_SING |
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where ![]() |
A | |
SIMP_MIN_NATURAL |
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A | ||
SIMP_MIN_NATURAL1 |
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A | ||
SIMP_MIN_BUNION_SING |
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A | ||
SIMP_MAX_BUNION_SING |
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A | ||
SIMP_MIN_UPTO |
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A | ||
SIMP_MAX_UPTO |
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A | ||
SIMP_LIT_MIN |
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where ![]() ![]() ![]() |
A | |
SIMP_LIT_MAX |
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where ![]() ![]() ![]() |
A | |
SIMP_LIT_MIN_UPTO |
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where ![]() |
A | |
SIMP_LIT_MAX_UPTO |
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where ![]() |
A | |
* | SIMP_SPECIAL_CARD |
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A | |
* | SIMP_CARD_SING |
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where ![]() |
A |
* | SIMP_SPECIAL_EQUAL_CARD |
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A | |
* | SIMP_CARD_POW |
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A | |
* | SIMP_CARD_BUNION |
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A | |
SIMP_CARD_CONVERSE |
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A | ||
SIMP_CARD_ID |
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where ![]() ![]() |
A | |
SIMP_CARD_ID_DOMRES |
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A
| ||
SIMP_CARD_LAMBDA |
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where ![]() ![]() ![]() ![]() |
A | |
SIMP_CARD_COMPSET |
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where ![]() ![]() |
A | |
* | SIMP_LIT_CARD_UPTO |
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where ![]() ![]() ![]() |
A |
SIMP_TYPE_CARD |
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where ![]() ![]() |
A | |
SIMP_LIT_GE_CARD_1 |
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A | ||
SIMP_LIT_LE_CARD_1 |
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A | ||
SIMP_LIT_LE_CARD_0 |
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A | ||
SIMP_LIT_GE_CARD_0 |
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A | ||
* | SIMP_LIT_GT_CARD_0 |
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A | |
* | SIMP_LIT_LT_CARD_0 |
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A | |
* | SIMP_LIT_EQUAL_CARD_1 |
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A | |
SIMP_CARD_NATURAL |
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A | ||
SIMP_CARD_NATURAL1 |
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A | ||
SIMP_LIT_IN_NATURAL |
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where ![]() |
A | |
SIMP_SPECIAL_IN_NATURAL1 |
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A | ||
SIMP_LIT_IN_NATURAL1 |
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where ![]() |
A | |
SIMP_LIT_UPTO |
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where ![]() ![]() ![]() |
A | |
SIMP_LIT_IN_MINUS_NATURAL |
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where ![]() |
A | |
SIMP_LIT_IN_MINUS_NATURAL1 |
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where ![]() |
A | |
* | DEF_IN_NATURAL |
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M | |
* | DEF_IN_NATURAL1 |
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M | |
SIMP_SPECIAL_KBOOL_BTRUE |
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A | ||
SIMP_SPECIAL_KBOOL_BFALSE |
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A | ||
* | SIMP_LIT_EQUAL_KBOOL_TRUE |
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A | |
* | SIMP_LIT_EQUAL_KBOOL_FALSE |
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A | |
DEF_EQUAL_MIN |
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where ![]() ![]() |
M | |
DEF_EQUAL_MAX |
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where ![]() ![]() |
M | |
* | SIMP_SPECIAL_PLUS |
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A | |
* | SIMP_SPECIAL_MINUS_R |
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A | |
* | SIMP_SPECIAL_MINUS_L |
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A | |
* | SIMP_MINUS_MINUS |
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A | |
* | SIMP_MINUS_UNMINUS |
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where ![]() |
M |
* | SIMP_MULTI_MINUS |
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A | |
* | SIMP_MULTI_MINUS_PLUS_L |
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M | |
* | SIMP_MULTI_MINUS_PLUS_R |
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M | |
* | SIMP_MULTI_MINUS_PLUS_PLUS |
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M | |
* | SIMP_MULTI_PLUS_MINUS |
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M | |
* | SIMP_MULTI_ARITHREL_PLUS_PLUS |
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where the root relation (![]() ![]() |
M |
* | SIMP_MULTI_ARITHREL_PLUS_R |
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where the root relation (![]() ![]() |
M |
* | SIMP_MULTI_ARITHREL_PLUS_L |
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where the root relation (![]() ![]() |
M |
* | SIMP_MULTI_ARITHREL_MINUS_MINUS_R |
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where the root relation (![]() ![]() |
M |
* | SIMP_MULTI_ARITHREL_MINUS_MINUS_L |
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where the root relation (![]() ![]() |
M |
* | SIMP_SPECIAL_PROD_0 |
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A | |
* | SIMP_SPECIAL_PROD_1 |
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A | |
* | SIMP_SPECIAL_PROD_MINUS_EVEN |
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if an even number of ![]() |
A |
* | SIMP_SPECIAL_PROD_MINUS_ODD |
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if an odd number of ![]() |
A |
* | SIMP_LIT_MINUS |
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where ![]() |
A |
* | SIMP_LIT_EQUAL |
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where ![]() ![]() |
A |
* | SIMP_LIT_LE |
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where ![]() ![]() |
A |
* | SIMP_LIT_LT |
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where ![]() ![]() |
A |
* | SIMP_LIT_GE |
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where ![]() ![]() |
A |
* | SIMP_LIT_GT |
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where ![]() ![]() |
A |
* | SIMP_DIV_MINUS |
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A | |
* | SIMP_SPECIAL_DIV_1 |
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A | |
* | SIMP_SPECIAL_DIV_0 |
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A | |
* | SIMP_SPECIAL_EXPN_1_R |
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A | |
* | SIMP_SPECIAL_EXPN_1_L |
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A | |
* | SIMP_SPECIAL_EXPN_0 |
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A | |
* | SIMP_MULTI_LE |
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A | |
* | SIMP_MULTI_LT |
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A | |
* | SIMP_MULTI_GE |
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A | |
* | SIMP_MULTI_GT |
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A | |
* | SIMP_MULTI_DIV |
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A | |
* | SIMP_MULTI_DIV_PROD |
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A | |
SIMP_MULTI_MOD |
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A | ||
DISTRI_PROD_PLUS |
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M | ||
DISTRI_PROD_MINUS |
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M | ||
DERIV_NOT_EQUAL |
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![]() ![]() |
M |