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Commit d15da6d4 by MARCHE Claude

### more lemmas on absolute value and subtraction

parent c74f2024
 ... @@ -32,6 +32,9 @@ theory Group ... @@ -32,6 +32,9 @@ theory Group clone Assoc with type t = t, function op = op clone Assoc with type t = t, function op = op axiom Inv_def : forall x:t. op x (inv x) = unit axiom Inv_def : forall x:t. op x (inv x) = unit lemma Inv_unit : forall x y:t. op x (inv y) = unit -> x = y end end theory CommutativeGroup theory CommutativeGroup ... ...
 ... @@ -19,8 +19,12 @@ theory Abs ... @@ -19,8 +19,12 @@ theory Abs function abs (x:int) : int = if x >= 0 then x else -x function abs (x:int) : int = if x >= 0 then x else -x lemma Abs_le: forall x y:int. abs x <= y <-> -y <= x <= y lemma Abs_pos: forall x:int. abs x >= 0 lemma Abs_pos: forall x:int. abs x >= 0 lemma Abs_zero: forall x:int. abs x = 0 -> x = 0 end end theory MinMax theory MinMax ... ...
 ... @@ -11,6 +11,8 @@ theory Real ... @@ -11,6 +11,8 @@ theory Real clone export algebra.OrderedField with type t = real, clone export algebra.OrderedField with type t = real, function zero = zero, function one = one, predicate (<=) = (<=) function zero = zero, function one = one, predicate (<=) = (<=) lemma sub_zero: forall x y:real. x - y = 0.0 -> x = y end end theory RealInfix theory RealInfix ... @@ -40,6 +42,8 @@ theory Abs ... @@ -40,6 +42,8 @@ theory Abs lemma Abs_pos: forall x:real. abs x >= 0.0 lemma Abs_pos: forall x:real. abs x >= 0.0 lemma Abs_zero: forall x:real. abs x = 0.0 -> x = 0.0 end end theory MinMax theory MinMax ... ...
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