*)
definition if_then_else ≝ λT:Type.λe,t,f.match e return λ_.T with [ true ⇒ t | false ⇒ f].
notation > "'if' term 19 e 'then' term 19 t 'else' term 90 f" non associative with precedence 90 for @{ 'if_then_else $e $t $f }.
-notation < "'if' \nbsp term 19 e \nbsp 'then' \nbsp term 19 t \nbsp 'else' \nbsp term 90 f \nbsp" non associative with precedence 90 for @{ 'if_then_else _ $e $t $f }.
+notation < "'if' \nbsp term 19 e \nbsp 'then' \nbsp term 19 t \nbsp 'else' \nbsp term 90 f \nbsp" non associative with precedence 90 for @{ 'if_then_else $e $t $f }.
interpretation "Formula if_then_else" 'if_then_else e t f = (if_then_else _ e t f).
notation < "[[ \nbsp term 19 a \nbsp ]] \nbsp \sub term 90 v" non associative with precedence 90 for @{ 'semantics $v $a }.
notation > "[[ term 19 a ]] \sub term 90 v" non associative with precedence 90 for @{ 'semantics $v $a }.