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Problem 4. Prove by induction on the complexity of formula that A[x := x] is always defined and equal to A, for any first-order formula A and variable x. (You can use that the fact t[x := x] is t for any term t without proving it.)

Problem 4. Prove by induction on the complexity of formula that A[x := x] is always defined and equal to A, for any first-order formula A and variable x. (You can use that the fact t[x := x] is t for any term t without proving it.)

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter14: Sequences And Mathematical Induction
Section14.4: Mathematical Induction
Problem 11PS
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Problem 4. Prove by induction on the complexity of formula that A[x := x] is always defined and equal to A, for any first-order formula A and variable x. (You can use that the fact t[x := x] is t for any term t without proving it.)
Transcribed Image Text:Problem 4. Prove by induction on the complexity of formula that A[x := x] is always defined and equal to A, for any first-order formula A and variable x. (You can use that the fact t[x := x] is t for any term t without proving it.)
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