[Merged by Bors] - feat(analysis): Cauchy sequence and series lemmas #7858
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from LTE. Mostly relaxing assumptions from metric to pseudo-metric and priving some obvious lemmas.
eric-wieser
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Jun 9, 2021
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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Is it reasonable to have something like |
sgouezel
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Jun 10, 2021
src/analysis/specific_limits.lean
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| variables [semi_normed_group α] {r C : ℝ} {f : ℕ → α} | ||
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| lemma normed_group.cauchy_seq_of_le_geometric {C : ℝ} {r : ℝ} (hr : r < 1) | ||
| {u : ℕ → α} (h : ∀ n, ∥u n - u (n + 1)∥ ≤ C*r^n) : cauchy_seq u := |
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Suggested change
| {u : ℕ → α} (h : ∀ n, ∥u n - u (n + 1)∥ ≤ C*r^n) : cauchy_seq u := | |
| {u : ℕ → α} (h : ∀ n, ∥u n - u (n + 1)∥ ≤ C*r^n) : cauchy_seq u := |
| end | ||
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| lemma normed_group.cauchy_series_of_le_geometric'' {C : ℝ} {u : ℕ → α} {N : ℕ} {r : ℝ} | ||
| (hr₀ : 0 < r) (hr₁ : r < 1) |
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I got tired of lemmas where most of the proof deals with weakening such constraint whereas they are never an issue when applying the lemma. Look at the previous lemma. Most of the proof is showing we can assume C and r are positive.
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from LTE. Mostly relaxing assumptions from metric to
pseudo-metric and proving some obvious lemmas.
eventually_constant_prod and eventually_constant_sum are duplicated by hand because `to_additive` gets confused by the appearance of `1`.
In `norm_le_zero_iff' {G : Type*} [semi_normed_group G] [separated_space G]` and the following two lemmas the type classes assumptions look silly, but those lemmas are indeed useful in some specific situation in LTE.
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from LTE. Mostly relaxing assumptions from metric to
pseudo-metric and proving some obvious lemmas.
eventually_constant_prod and eventually_constant_sum are duplicated by hand because `to_additive` gets confused by the appearance of `1`.
In `norm_le_zero_iff' {G : Type*} [semi_normed_group G] [separated_space G]` and the following two lemmas the type classes assumptions look silly, but those lemmas are indeed useful in some specific situation in LTE.
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bors bot
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from LTE. Mostly relaxing assumptions from metric to
pseudo-metric and proving some obvious lemmas.
eventually_constant_prod and eventually_constant_sum are duplicated by hand because `to_additive` gets confused by the appearance of `1`.
In `norm_le_zero_iff' {G : Type*} [semi_normed_group G] [separated_space G]` and the following two lemmas the type classes assumptions look silly, but those lemmas are indeed useful in some specific situation in LTE.
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Build failed (retrying...): |
bors bot
pushed a commit
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Jun 11, 2021
from LTE. Mostly relaxing assumptions from metric to
pseudo-metric and proving some obvious lemmas.
eventually_constant_prod and eventually_constant_sum are duplicated by hand because `to_additive` gets confused by the appearance of `1`.
In `norm_le_zero_iff' {G : Type*} [semi_normed_group G] [separated_space G]` and the following two lemmas the type classes assumptions look silly, but those lemmas are indeed useful in some specific situation in LTE.
bors bot
pushed a commit
that referenced
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Jun 11, 2021
from LTE. Mostly relaxing assumptions from metric to
pseudo-metric and proving some obvious lemmas.
eventually_constant_prod and eventually_constant_sum are duplicated by hand because `to_additive` gets confused by the appearance of `1`.
In `norm_le_zero_iff' {G : Type*} [semi_normed_group G] [separated_space G]` and the following two lemmas the type classes assumptions look silly, but those lemmas are indeed useful in some specific situation in LTE.
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from LTE. Mostly relaxing assumptions from metric to
pseudo-metric and proving some obvious lemmas.
eventually_constant_prod and eventually_constant_sum are duplicated by hand because
to_additivegets confused by the appearance of1.In
norm_le_zero_iff' {G : Type*} [semi_normed_group G] [separated_space G]and the following two lemmas the type classes assumptions look silly, but those lemmas are indeed useful in some specific situation in LTE.