Commit d15da6d4 authored by MARCHE Claude's avatar MARCHE Claude

more lemmas on absolute value and subtraction

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