We describe the mechanization of recent examples of compositional reasoning, due to Charpentier and Chandy [4]. The examples illustrate a new theory for composition proposed by Chandy and Sanders [2, 3], based on the so-called existential and universal properties. We show that, while avoiding hand proof mistakes, a such compositional reasoning can be mechanized quite straightforwardly. We also ...

The effective action for type II string theory compactified on a six torus is N = 8 supergravity, which is known to have an E 7 duality symmetry. We show that this is broken by quantum effects to a discrete subgroup, E 7 (Z), which contains both the T-duality group O(6, 6; Z) and the S-duality group SL(2; Z). We present evidence for the conjecture that E 7 (Z) is an exact 'U-duality' symmetry o...

(2) Let D be a non empty set, S be a non empty subset of D, f be a binary operation on D, g be a binary operation on S, d be an element of D, and d′ be an element of S such that g = f [:S, S :] and d′ = d. Then (i) if d is a left unity w.r.t. f , then d′ is a left unity w.r.t. g, (ii) if d is a right unity w.r.t. f , then d′ is a right unity w.r.t. g, and (iii) if d is a unity w.r.t. f , then d...

the fundamental belief in sikhism is that god exists not merely as an idea or concept, but as a real entity. god is indescribable, yet knowable and perceivable to anyone who is prepared to dedicate the time and energy to become perceptive to his persona. the gurus never spoke about proofs of the existence of god. for them, he is too real, and something obvious does not require any logical proof...