diff --git a/MIL/C08_Topology/S02_Metric_Spaces.lean b/MIL/C08_Topology/S02_Metric_Spaces.lean index 245d2c9d..073c20df 100644 --- a/MIL/C08_Topology/S02_Metric_Spaces.lean +++ b/MIL/C08_Topology/S02_Metric_Spaces.lean @@ -432,7 +432,7 @@ theorem cauchySeq_of_le_geometric_two' {u : ℕ → X} dist (u (N + k)) (u N) = dist (u (N + 0)) (u (N + k)) := sorry _ ≤ ∑ i in range k, dist (u (N + i)) (u (N + (i + 1))) := sorry _ ≤ ∑ i in range k, (1 / 2 : ℝ) ^ (N + i) := sorry - _ = 1 / 2 ^ N * ∑ i in range k, (1 / 2) ^ i := sorry + _ = 1 / 2 ^ N * ∑ i in range k, (1 / 2 : ℝ) ^ i := sorry _ ≤ 1 / 2 ^ N * 2 := sorry _ < ε := sorry