0

enter image description here

Hey guys. So I have H0, I got my x and H1. as far as I understand, if ill show that there is an x for which P x -> False, ill get a False and can discriminate the case. I just dont understand how to provide that x and H1. I tried rewrite, apply and im just stuck.

user615297
  • 11
  • 3
  • 2
    Hi and welcome to Coq ! Could you provide a minimal working example with code insert rather than an image ? It helps helping you out in your proof :) You might be looking for the `exfalso` (turns your goal into `False`) and `exists` tactics. – cbl Dec 21 '21 at 23:04
  • Welcome to Stack Overflow _ As requested by @cbl please take a moment to translate the text in your image into a code block within your post _ Please take a moment to visit SO Help Center's 'Asking' section and specifically this link >>> https://stackoverflow.com/help/minimal-reproducible-example – inputforcolor Dec 30 '21 at 14:10

1 Answers1

2

As mentioned by cbl, you first use exfalso to turn your goal into False. Then you apply H0 which leaves you with exists x0 : X, P x0 -> False. Then you use exists x which leaves you with H1, so that you can solve the goal with exact H1.

M Soegtrop
  • 1,268
  • 2
  • 8
  • Thanks, I did what you and cbl suggested, it solved my problem. there is no way to supply the exists x0 and P x0 -> False into H1 directly without using exfalso? – user615297 Dec 22 '21 at 14:56
  • Well yes, you can do `specialize (H0 (ex_intro _ _ H1)).` This will turn H0 into False. It helps to turn off notations in your IDE to see what the exists really is - it becomes obvious then. – M Soegtrop Dec 22 '21 at 17:03