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Question: How to prove this equality under given conditions?

Question:How to prove this equality under given conditions?

mmcdara 6740 Maple 2015
simplification
July 28 2023
0


How to force Maple to prove equality (2) under conditions cond.

 

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restart:
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# Given
#     0 < u < 1
#     0 < v < 1
#     theta > 1
#
# let F the function defined by:

F := (u, v) -> exp(-((-ln(u))^theta+(-ln(v))^theta)^(1/theta))

proc (u, v) options operator, arrow; exp(-((-ln(u))^theta+(-ln(v))^theta)^(1/theta)) end proc

 (1)
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# How to prove this equality for any n > 0?

'F(u^(1/n), v^(1/n))^n' = 'F(u, v)'

F(u^(1/n), v^(1/n))^n = F(u, v)

 (2)
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cond := u > 0, u < 1, v > 0, v < 1, theta > 1, n > 1:

simplify(F(u^(1/n), v^(1/n))^n - F(u, v)) assuming cond;

(exp(-(((-ln(u))^theta+(-ln(v))^theta)*n^(-theta))^(1/theta)))^n-exp(-((-ln(u))^theta+(-ln(v))^theta)^(1/theta))

 (3)
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