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The number and length of substitutions were obtained by observation.

Substitution in English Grammar

An average of Within the first minute of substitution, re-entering players covered a significantly larger total distance A significant decrease in physical performance was observed within the fifth minute after substitution. Further, re-entering field hockey players experienced distinguishable signs of fatigue approximately four minutes after substitution. Skip to Main Content.

Search in: This Journal Anywhere. Advanced search. The resulting expression is called a substitution instance , or short instance , of the original expression. For example:.

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In some deduction systems for propositional logic, a new expression a proposition may be entered on a line of a derivation if it is a substitution instance of a previous line of the derivation Hunter , p. This is how new lines are introduced in some axiomatic systems.

see In systems that use rules of transformation , a rule may include the use of a substitution instance for the purpose of introducing certain variables into a derivation. In first-order logic , every closed propositional formula that can be derived from an open propositional formula a by substitution is said to be a substitution instance of a. If a is a closed propositional formula we count a itself as its only substitution instance.

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  • A propositional formula is a tautology if it is true under every valuation or interpretation of its predicate symbols. This fact implies the soundness of the deduction rule described in the previous section. A substitution is called a ground substitution if it maps all variables of its domain to ground , i.

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    However, it is not possible to define an inverse for an arbitrary substitution. Composition is an associative operation, and is compatible with substitution application, i.

    Football Players Angry After Substitution

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    • Should you need to do a double substitution follow the same procedure.