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A-conversion algorithm application argument atoms axiom schemes basis binary operation bound variables called Chapter Church Church-Rosser theorem combinatory logic completes the proof component consider consistency consistency proof construction contains contraction conversion corresponding deductive induction definiendum definiens defining axioms definition derived elementary statements elementary theorem epistatements epitheorems equivalent example F-deduction F-inference F-obs F-simple finite follows formal system functional character given Hence holds hypothesis indeterminates inference infix instance interpretation intuitive Kleene Lemma minor premise normal form notation notion obtained occur free Oi-ob operation parentheses postulates predicate premise primitive combinators primitive frame proof of Theorem prove quasi-ordering recursive redex reduction rule regular combinator relation relative replacement respect restricted Rosser Rule Eq Rule F sense sequence step stratification strong reduction structural induction substitution suppose symbols T-rules theory of combinators Type U-language unique residual universal predicate valid