diff --git a/MathTest.lean b/MathTest.lean index 5be7cdf..6b1d913 100644 --- a/MathTest.lean +++ b/MathTest.lean @@ -1 +1,2 @@ import MathTest.Basic +import MathTest.Theorems.RationalSequenceExists diff --git a/MathTest/Theorems/RationalSequenceExists.lean b/MathTest/Theorems/RationalSequenceExists.lean new file mode 100644 index 0000000..ecf9136 --- /dev/null +++ b/MathTest/Theorems/RationalSequenceExists.lean @@ -0,0 +1,11 @@ +import Mathlib + +theorem rational_sequence_exists : + ∃ s : Nat → Rat, ∀ a d : Rat, ∃ t : Nat, s t = a + d * t := by + classical + obtain ⟨f, hf⟩ := exists_surjective_nat (α := Rat × Rat) + refine ⟨fun n => (f n).1 + (f n).2 * n, ?_⟩ + intro a d + obtain ⟨t, ht⟩ := hf ⟨a, d⟩ + refine ⟨t, ?_⟩ + simpa [ht] diff --git a/ttt b/ttt new file mode 100644 index 0000000..8e4ef39 --- /dev/null +++ b/ttt @@ -0,0 +1,1647 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + GitHub - winger/math-test + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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