Commit b3937b40 by Jean-Christophe Filliâtre

### new theory int.Sum

parent 996a6be6
 ... ... @@ -334,6 +334,44 @@ theory NumOf end (** {2 Sum} *) theory Sum use import Int use HighOrd function sum (a b: int) (f: int -> int) : int (** sum of [f n] for [a <= n <= b] *) axiom sum_def1: forall f: int -> int, a b: int. b < a -> sum a b f = 0 axiom sum_def2: forall f: int -> int, a b: int. a <= b -> sum a b f = sum a (b - 1) f + f b lemma sum_left: forall f: int -> int, a b: int. a <= b -> sum a b f = f a + sum (a + 1) b f lemma sum_ext: forall f g: int -> int, a b: int. (forall i. a <= i <= b -> f i = g i) -> sum a b f = sum a b g lemma sum_nonneg: forall f: int -> int, a b: int. (forall i. a <= i <= b -> 0 <= f i) -> 0 <= sum a b f lemma sum_decomp: forall f: int -> int, a b c: int. a <= b <= c -> sum a c f = sum a b f + sum (b+1) c f end (** {2 Factorial function} *) theory Fact ... ...
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