to do what you claimed and show proof; to prove what you're capable of
A equipe prometeu resolver e agora precisa matar a cobra e mostrar o pau.
The team promised a solution and now has to deliver it and show the proof.
The rural image is literal and evidential: after killing a snake, the person shows the stick used to do it. Figuratively, the second action supplies proof for the first, so the expression means accomplishing what was claimed and demonstrating it.
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