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Textual Substitution Equality and Assignment
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algorithm antecedent Arithmetic assignment Axiom binary operator boolean algebra boolean expression called circuit closed-form solution conjunct Consider construct contains defined denote Distributivity dummy edges English equal equational equivalent example Exercises existential quantification false finite following theorem formal formula graph Hence Hint Historical note holds Idempotency identity inductive definition inductive hypothesis inference rules infinite integers invariant inverse isomorphic iteration Leibniz logic loop manipulation mathematical induction mathematics Metatheorem minimal element monoid multiple mutual implication natural numbers nonempty notation one-to-one pair path permutations pigeonhole principle planar graph positive integers postcondition predicate predicate logic proof properties propositional calculus propositional logic prove the following Prove theorem quantification real numbers reflexive relation replaced satisfies sequence set comprehension spanning tree statement subset Symmetry textual substitution theory Transitivity true truth table universal quantification valid variables vertex vertices zero