# Library Coq.Init.Notations

These are the notations whose level and associativity are imposed by Coq
Notations for propositional connectives
Reserved Notation "x <-> y" (at level 95, no associativity).
Reserved Notation "x /\ y" (at level 80, right associativity).
Reserved Notation "x \/ y" (at level 85, right associativity).
Reserved Notation "~ x" (at level 75, right associativity).
Notations for equality and inequalities
Reserved Notation "x = y :> T"
(at level 70, y at next level, no associativity).
Reserved Notation "x = y" (at level 70, no associativity).
Reserved Notation "x = y = z"
(at level 70, no associativity, y at next level).
Reserved Notation "x <> y :> T"
(at level 70, y at next level, no associativity).
Reserved Notation "x <> y" (at level 70, no associativity).
Reserved Notation "x <= y" (at level 70, no associativity).
Reserved Notation "x < y" (at level 70, no associativity).
Reserved Notation "x >= y" (at level 70, no associativity).
Reserved Notation "x > y" (at level 70, no associativity).
Reserved Notation "x <= y <= z" (at level 70, y at next level).
Reserved Notation "x <= y < z" (at level 70, y at next level).
Reserved Notation "x < y < z" (at level 70, y at next level).
Reserved Notation "x < y <= z" (at level 70, y at next level).
Arithmetical notations (also used for type constructors)
Reserved Notation "x + y" (at level 50, left associativity).
Reserved Notation "x - y" (at level 50, left associativity).
Reserved Notation "x * y" (at level 40, left associativity).
Reserved Notation "x / y" (at level 40, left associativity).
Reserved Notation "- x" (at level 35, right associativity).
Reserved Notation "/ x" (at level 35, right associativity).
Reserved Notation "x ^ y" (at level 30, right associativity).
Notations for booleans
Reserved Notation "x || y" (at level 50, left associativity).
Reserved Notation "x && y" (at level 40, left associativity).
Notations for pairs
Reserved Notation "( x , y , .. , z )" (at level 0).
Notation "{ x }" is reserved and has a special status as component of other notations such as "{ A } + { B }" and "A + { B }" (which are at the same level than "x + y"); "{ x }" is at level 0 to factor with "{ x : A | P }"
Reserved Notation "{ x }" (at level 0, x at level 99).
Notations for sigma-types or subsets
Reserved Notation "{ x | P }" (at level 0, x at level 99).
Reserved Notation "{ x | P & Q }" (at level 0, x at level 99).
Reserved Notation "{ x : A | P }" (at level 0, x at level 99).
Reserved Notation "{ x : A | P & Q }" (at level 0, x at level 99).
Reserved Notation "{ x : A & P }" (at level 0, x at level 99).
Reserved Notation "{ x : A & P & Q }" (at level 0, x at level 99).
Delimit Scope type_scope with type.
Delimit Scope core_scope with core.
Open Scope core_scope.
Open Scope type_scope.