[Merged by Bors] - feat: dot notation for IsTheta.add_isLittleO, and add_commed variants
#10386
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…iants BREAKING CHANGE: Change `IsTheta.add_isLittleO` into a dot-notation statement, in line with the existing `IsBigO`. Move the current `IsTheta.add_isLittleO` statement to `IsLittleO.left_isTheta_add`, in line with the existing `IsLittleO.left_isIsBigO_add`. feat: Add `add_comm`ed variants of related lemmas. These changes smoothen the flow when proving e.g. `a + b + c + d + e + f =Θ[l] d`.
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| @@ -2137,6 +2137,10 @@ theorem IsLittleO.right_isBigO_add {f₁ f₂ : α → E'} (h : f₁ =o[l] f₂) | |||
| ((h.def' one_half_pos).right_le_add_of_lt_one one_half_lt_one).isBigO | |||
| #align asymptotics.is_o.right_is_O_add Asymptotics.IsLittleO.right_isBigO_add | |||
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| theorem IsLittleO.right_isBigO_add' {f₁ f₂ : α → E'} (h : f₁ =o[l] f₂) : | |||
| f₂ =O[l] (f₂ + f₁) := | |||
| Trans.trans h.right_isBigO_add (add_comm _ _) | |||
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Does this work? Untested...
Suggested change
| Trans.trans h.right_isBigO_add (add_comm _ _) | |
| h.right_isBigO_add.trans (add_comm _ _) |
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Unfortunately not, since this is IsBigO trans Eq, whereas IsBigO.trans is IsBigO trans IsBigO. There is also no IsBigO.trans_eq lemma; instead there is this instance for Trans.trans: https://github.com/leanprover/lean4/blob/56d703db8eec777b813a198e2126115bda9d3a9b/src/Init/Prelude.lean#L1152-L1153
EDIT: I can, however, copy from the linked proof: add_comm f₁ f₂ ▸ h.right_isBigO_add
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| theorem IsLittleO.right_isTheta_add' {f₁ f₂ : α → E'} (h : f₁ =o[l] f₂) : | ||
| f₂ =Θ[l] (f₂ + f₁) := | ||
| Trans.trans h.right_isTheta_add (add_comm _ _) |
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Idem
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| Trans.trans h.right_isTheta_add (add_comm _ _) | |
| h.right_isTheta_add.trans (add_comm _ _) |
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I'm not a big fan of using |
👍 I'll wait for ideas here. It might involve renaming both this new |
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IsTheta.add_isLittleO, and add_commed variantsIsTheta.add_isLittleO, and add_commed variants
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…ants (#10386) BREAKING CHANGE: Change `IsTheta.add_isLittleO` into a dot-notation statement, in line with the existing `IsBigO.add_isLittleO`. Move the current `IsTheta.add_isLittleO` statement to `IsLittleO.right_isTheta_add'`, in line with the existing `IsLittleO.right_isBigO_add`. feat: Add `add_comm`ed variants of related lemmas. These changes smoothen the flow when proving e.g. `a + b + c + d + e + f =Θ[l] d`. Co-authored-by: L Lllvvuu <git@llllvvuu.dev>
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Pull request successfully merged into master. Build succeeded: |
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IsTheta.add_isLittleO, and add_commed variantsIsTheta.add_isLittleO, and add_commed variants
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…ants (#10386) BREAKING CHANGE: Change `IsTheta.add_isLittleO` into a dot-notation statement, in line with the existing `IsBigO.add_isLittleO`. Move the current `IsTheta.add_isLittleO` statement to `IsLittleO.right_isTheta_add'`, in line with the existing `IsLittleO.right_isBigO_add`. feat: Add `add_comm`ed variants of related lemmas. These changes smoothen the flow when proving e.g. `a + b + c + d + e + f =Θ[l] d`. Co-authored-by: L Lllvvuu <git@llllvvuu.dev>
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…ants (#10386) BREAKING CHANGE: Change `IsTheta.add_isLittleO` into a dot-notation statement, in line with the existing `IsBigO.add_isLittleO`. Move the current `IsTheta.add_isLittleO` statement to `IsLittleO.right_isTheta_add'`, in line with the existing `IsLittleO.right_isBigO_add`. feat: Add `add_comm`ed variants of related lemmas. These changes smoothen the flow when proving e.g. `a + b + c + d + e + f =Θ[l] d`. Co-authored-by: L Lllvvuu <git@llllvvuu.dev>
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BREAKING CHANGE: Change
IsTheta.add_isLittleOinto a dot-notation statement, in line with the existingIsBigO.add_isLittleO. Move the currentIsTheta.add_isLittleOstatement toIsLittleO.right_isTheta_add', in line with the existingIsLittleO.right_isBigO_add.feat: Add
add_commed variants of related lemmas.These changes smoothen the flow when proving e.g.
a + b + c + d + e + f =Θ[l] d.