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# <ConsistencyModule:> <=>(+ConX,+ConY,Bool)

Bool is the reified truth of constraint ConX is equivalent to the truth of ConY.
*ConX*
- Constraint
*ConY*
- Constraint
*Bool*
- Reified truth value of the constraint (array notation accepted)

## Description

Equivalent to BX #= (ConX), BY #= (ConY), Bool #= (BX #= BY)

The two constraints are reified in such a way that Bool is true if ConX
and ConY have the same truth value. ConX and ConY must be
constraints that have a corresponding reified form.

This reified connective is not available in IC because #=/3 can be
used instead. It is provided in GFD as <=> maps to gecode's
equivalence connective.
ConsistencyModule is the optional module specification to give the
consistency level for the propagation for this constraint:
gfd_bc for bounds consistency, and gfd_gac for domain (generalised arc)
consistency.

This constraint is implemented using Gecode's MiniModel's rel() for
both integer and boolean expressions, with sub-expressions/constraints
not supported by MiniModel factored out and posted as auxiliary
constraints.

A more restricted version of this constraint is defined in the
global constraint catalog as 'equivalent', in that the reified truth value
is the logical equivalence of 0/1 variables rather than constraints.

### Modules

This predicate is sensitive to its module context (tool predicate, see @/2).
## See Also

<=> / 2, neg / 2, => / 3, or / 3, xor / 3, and / 3, suspend : #\= / 3, ic : #\= / 3, fd : #\= / 3