“In evidence” is a phrase meaning “noticeable, conspicuous”
Today is calm and sunny, and all the autumn colours are still much in evidence.
"life being sat fifty." is obviously an error.
She's living proof of the saying that life begins at fifty.
“be (the) living proof that (or of)” is a phrase and means “to show by one's existence and qualities that something is the case”
She regarded the ring as proof positive of his love.
“proof positive” is an expression that means “absolute proof of the existence of something”
The proof of the pudding. (is in the eating)
It’s a proverb:
“The proof of the pudding is in the eating/The proof of the pudding/The proof is in the pudding.”
It means that you can only judge the quality of something after you have tried, used, or experienced it.
I’m unable to explain in a simple way the difference between “proof” and “evidence”.
This is the definition of “proof” from Wikipedia:
“A proof is sufficient evidence or a sufficient argument for the truth of a proposition.”
This is the definition from Oxford dictionaries:
Proof=evidence or argument establishing a fact or the truth of a statement.
“Evidence” can mean “signs or indications of something”:
‘there was no obvious evidence of a break-in’
I would say
“There is some evidence that the economy is improving.”