mathlib documentation

data.list.palindrome

Palindromes

This module defines palindromes, lists which are equal to their reverse.

The main result is the palindrome inductive type, and its associated palindrome.rec_on induction principle. Also provided are conversions to and from other equivalent definitions.

References

Tags

palindrome, reverse, induction

source
inductive palindrome {α : Type u_1} (a : list α) :
Prop

palindrome l asserts that l is a palindrome. This is defined inductively:

  • The empty list is a palindrome;
  • A list with one element is a palindrome;
  • Adding the same element to both ends of a palindrome results in a bigger palindrome.
source
theorem palindrome.reverse_eq {α : Type u_1} {l : list α} (p : palindrome l) :
l.reverse = l

source
theorem palindrome.of_reverse_eq {α : Type u_1} {l : list α} (a : l.reverse = l) :
palindrome l

source
theorem palindrome.iff_reverse_eq {α : Type u_1} {l : list α} :
palindrome l ↔ l.reverse = l

source
theorem palindrome.append_reverse {α : Type u_1} (l : list α) :
palindrome (l ++ l.reverse)

source
@[instance]
def palindrome.decidable {α : Type u_1} [decidable_eq α] (l : list α) :
decidable (palindrome l)

Equations