query: prove something must happen with pigeonhole principle
positive_passages.docid: 157462
positive_passages.text: If any $15$ cars have $3$ with the same manufacturer, prove that any $100$ cars have $15$ with the same manufacturer.
negative_passages.docid: 49994
negative_passages.text: Deduction of $\forall y \exists x (x=y)$
negative_passages.docid: 148790
negative_passages.text: Basic question about proofs with the goal $\exists x P(x)$
negative_passages.docid: 1508
negative_passages.text: How do I prove that a definition of an ordered pair does not satisfy the required property?
negative_passages.docid: 151356
negative_passages.text: Need Hints Prove "$((\neg \alpha \to \alpha) \to \alpha) $" Using Axiom 1,2,3 and MP and deduction theorem
negative_passages.docid: 103463
negative_passages.text: Mantel's Theorem proof verification
negative_passages.docid: 31091
negative_passages.text: Prove that there exist a branch
negative_passages.docid: 90828
negative_passages.text: Help proving exercise on sequences in Bartle's Elements
negative_passages.docid: 32181
negative_passages.text: A logic puzzle involving a balance.
negative_passages.docid: 42150
negative_passages.text: Prove that $\forall x \neg P(x) \iff \neg \exists x P(x)$
negative_passages.docid: 113344
negative_passages.text: How do we prove that something is unprovable?
negative_passages.docid: 48797
negative_passages.text: Proving Two Sets are Equal - Infinite Sets - Example
negative_passages.docid: 58481
negative_passages.text: Exclusion Inclusion Principle Induction Proof
negative_passages.docid: 115955
negative_passages.text: Prove the Probability of Two Events
negative_passages.docid: 134120
negative_passages.text: Prove statement with a counter-example: For all sets S, T and V, V ∪ (S ∩ T) = (V ∪ S) ∩ T is false
negative_passages.docid: 157625
negative_passages.text: How to prove conditional in Coq?
negative_passages.docid: 39382
negative_passages.text: Examples of the Pigeonhole Principle