include "logic/equality.ma".
-include "BNot/defs.ma".
+include "Bool/defs.ma".
-inductive BEq (b1:Bool): Bool \to Bool \to Prop \def
- | beq_false: \forall b2. (~b1 == b2) \to BEq b1 false b2
- | beq_true : BEq b1 true b1
+inductive BEq (A:Type) (a1:A): A \to Bool \to Prop \def
+ | beq_true : BEq A a1 a1 true
+ | beq_false: \forall a2. (a1 = a2 -> False) \to BEq A a1 a2 false
.
(*CSC: the URI must disappear: there is a bug now *)
-interpretation "boolean coimplication predicate" 'rel_coimp x y z =
- (cic:/matita/RELATIONAL/BEq/defs/BEq.ind#xpointer(1/1) x y z).
+interpretation "boolean equality" 'beq x y z =
+ (cic:/matita/RELATIONAL/BEq/defs/BEq.ind#xpointer(1/1) _ x y z).
-notation "hvbox(a break * b break == c)"
+notation "hvbox(a break -- b break == c)"
non associative with precedence 95
-for @{ 'rel_coimp $a $b $c}.
+for @{ 'beq $a $b $c}.