Crossword Genius

Parade statement that becomes true on April Fool's day (5,4)

Ross

I believe the answer is:

march past

I'm a little stuck... Click here to teach me more about this clue!

'parade statement that becomes true on april fool's day' is the definition.
'march past' can be an answer for 'parade' (type of military parade). I am not sure about the rest of the definition.

'parade statement' is the wordplay.
'parade' becomes 'march' (a ceremonial march).
'statement' becomes 'past' (I can't justify this - if you can you should believe this answer much more).
'march'+'past'='MARCH PAST'

Can you help me to learn more?

(Other definitions for march past that I've seen before include "Companion" , "in previous tax year?" , "Review of forces" , "Army manoeuvre" , "Movement of a body of soldiers being reviewed" .)

I've seen this clue in The Times.
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