We learnt in class/Notes that A[x] → (Vx)A[x] is NOT a theorem if x indeed occurs free in A. Yet, I think I got a proof: First, let me use DThm and prove instead A[x] F (Væ)A[x]: 1) A[a] (hyp) 2) (Vx)A[a] (1 + Gen) 2.
We learnt in class/Notes that A[x] → (Vx)A[x] is NOT a theorem if x indeed occurs free in A. Yet, I think I got a proof: First, let me use DThm and prove instead A[x] F (Væ)A[x]: 1) A[a] (hyp) 2) (Vx)A[a] (1 + Gen) 2.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![We learnt in class/Notes that A[x] → (Vx)A[x] is NOT
theorem if x indeed occurs free in A.
Yet, I think I got a proof: First, let me use DThm and prove instead
A[x] F (Væ)A[x]:
1) A[a]
2) (Vx)A[x] (1 + Gen)
(hyp)
Something must be wrong in my “PROOF"! What EXACTLY (not too
many words please and above all don't say "it's not a theorem"!)
2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb2d2659c-073c-4d9b-b022-db6863ac78eb%2F2e946cd4-ae67-43d3-ac0b-0861c78a0399%2Fg71dim_processed.png&w=3840&q=75)
Transcribed Image Text:We learnt in class/Notes that A[x] → (Vx)A[x] is NOT
theorem if x indeed occurs free in A.
Yet, I think I got a proof: First, let me use DThm and prove instead
A[x] F (Væ)A[x]:
1) A[a]
2) (Vx)A[x] (1 + Gen)
(hyp)
Something must be wrong in my “PROOF"! What EXACTLY (not too
many words please and above all don't say "it's not a theorem"!)
2.
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