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public/beyond-booleans/index.md
··· 168 168 169 169 ### Proof Irrelevance 170 170 171 - It is worth noting that, just like a proposition may have *no* valid proofs, it may also have *many* proofs--in fact, as many as you like. For example, `2 + 2 = 4` can be proven `by rfl` but it can also be proven using an existing result from Mathlib (conveniently called `two_plus_to_eq_four`), or the more powerful `by decide`: 171 + It is worth noting that, just like a proposition may have *no* valid proofs, it may also have *many* proofs--in fact, as many as you like. For example, `2 + 2 = 4` can be proven `by rfl` but it can also be proven using an existing result from Mathlib (conveniently called `two_add_two_eq_four`), or the more powerful `by decide`: 172 172 173 173 ```lean 174 174 import Mathlib