By Saul A. Basri

ISBN-10: 0444534091

ISBN-13: 9780444534095

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**Additional info for A deductive theory of space and time (no TOC)**

**Sample text**

1. In fact, we may not be able to check t h e m at all, because too much information is missing. But we can collect equality constraints t h a t need to hold in order for t h e proof to be correct. Such equality constraints are of t h e form Ti = ' T2, where Ti and T2 are either both terms or b o t h types. A substitution solves a constraint if t h e two terms become equal modulo /377-conversion, or if t h e two types become identical. Sets of such equality constraints are usually denoted by t h e letters C and D.

Berghofer and T. Nipkow step 2, remaining subgoal: /\y. 3x. \/y. P x y ==> 3x. P x y Xg • (/\y. 3x. 'iy. P x y = > 3x. P x y). impi (3a:. Vy. P x y) (Vy. 3x. P x y) (A/ii : (3a;. Vj,. P x y). alll (Ay. 3a;. P x y) (Ay :: /?. g y fei)) By eliminating the existence quantifier using exE we get step 3, remaining subgoal: / \ y x. Vy. P a; y =^ 3x. \iy. P X y =^ 3x. P x y). impI (3a;. Vy. P x y) {Vy. 3a;. P x y) (A/ii : (3a;. Vy. P x y). alll (Ay. 3a;. P a; y) (Ay :: /3. exE (Aa;. Vy. P a; y) (3a;. P x y) hi (yy))) Applying the introduction rule ex!

J. Levy. Explicit substitutions. In Conference Record of the Seventeenth Annual ACM Symposium on Principles of Programming Languages, San Francisco, California, pages 31-46. ACM, January 1990. Also Digital Equipment Corporation, Systems Research Center, Research Report 54, February 1990. 2. H. Barendregt. Lambda Calculi with Types. Technical Report 91-19, Catholic University Nijmegen, 1991. In Handbook of Logic in Computer Science, Vol II. 3. B. Barras. Auto-validation d'un systeme de preuves avec families inductives.

### A deductive theory of space and time (no TOC) by Saul A. Basri

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