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doc: demote repeated H1 headers (leanprover-community#36833)
Having more than one H1 header per file confuses search engines and thus makes documentation more difficult to find. Hence, we make sure that lean files only have a single H1 header in them. In the case of `Mathlib/Tactic/Common.lean`, we achieve this by adding a new module header.
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Archive/Imo/Imo2002Q3.lean

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@@ -12,7 +12,7 @@ import Mathlib.RingTheory.Polynomial.Content
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Find all pairs of positive integers $m,n ≥ 3$ for which there exist infinitely many
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positive integers $a$ such that $(a^m+a-1) / (a^n+a^2-1)$ is itself an integer.
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# Solution
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## Solution
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It suffices to find $(m,n)$ pairs for which $a^n+a^2-1 ∣ a^m+a-1$, where both sides are viewed as
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polynomials in $a$. This automatically gives $n ≤ m$, so we have

Archive/Imo/Imo2010Q5.lean

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@@ -25,7 +25,7 @@ Determine if there exists a finite sequence of operations of the allowed types,
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that the five boxes $B_1, B_2, B_3, B_4, B_5$ become empty, while box $B_6$ contains exactly
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$2010^{2010^{2010}}$ coins.
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# Solution
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## Solution
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We follow the solution from https://web.evanchen.cc/exams/IMO-2010-notes.pdf.
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Mathlib/Geometry/Manifold/VectorBundle/LocalFrame.lean

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@@ -439,7 +439,7 @@ lemma localFrame_coeff_eq_coeff (hxe : x ∈ e.baseSet) {i : ι} :
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end Bundle.Trivialization
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/-! # Determining smoothness of a section via its local frame coefficients
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/-! ### Determining smoothness of a section via its local frame coefficients
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We show that for finite rank bundles over a complete field, a section is smooth iff its coefficients
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in a local frame induced by a local trivialisation are. In many contexts, this statement holds for
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*any* local frame (e.g., for all real bundles which admit a continuous bundle metric, as is

Mathlib/Probability/Distributions/Gaussian/HasGaussianLaw/Basic.lean

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@@ -15,7 +15,7 @@ import Mathlib.Probability.Distributions.Gaussian.Fernique
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In this file we prove basic properties of Gaussian random variables.
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# Implementation note
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## Implementation note
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Many lemmas are duplicated with an expanded form of some function. For instance there is
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`HasGaussianLaw.add` and `HasGaussianLaw.fun_add`. The reason is that if someone wants for instance

Mathlib/RingTheory/LocalProperties/Injective.lean

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@@ -15,7 +15,7 @@ public import Mathlib.RingTheory.LocalProperties.Exactness
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# Being injective is a local property
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# Main Results
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## Main Results
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* `Module.injective_of_isLocalizedModule` : For module `M` over Noetherian ring `R`,
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being injective is preserved under localization.

Mathlib/RingTheory/LocalProperties/ProjectiveDimension.lean

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In this file, we proved that projective dimension equal to supremum over localizations
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# Main definition and results
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## Main definition and results
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-/
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Mathlib/RingTheory/QuasiFinite/Weakly.lean

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@@ -20,7 +20,7 @@ equivalent to `Algebra.QuasiFiniteAt` under all relevant scenarios.
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This class should only be used in stating (and proving) Zariski's main theorem and should not be
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used elsewhere, and all public API shall have a `Algebra.QuasiFiniteAt` version.
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# Implementation details
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## Implementation details
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The definition of `Algebra.QuasiFiniteAt R q` as is says that the whole `S_q` is quasi-finite,
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which requires not only `q` to be quasi-finite, but also all primes below it (i.e. all generic

Mathlib/Tactic/Common.lean

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public import Mathlib.Util.WhatsNew
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/-!
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# Common tactics, linters, and utilities
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This file imports all tactics which do not have significant theory imports,
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and hence can be imported very low in the theory import hierarchy,
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thereby making tactics widely available without needing specific imports.
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public meta section
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/-!
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# Register tactics with `hint`. Tactics with larger priority run first.
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### Register tactics with `hint`. Tactics with larger priority run first.
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section Hint
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end Hint
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/-!
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# Register tactics with `try?`. Tactics with larger priority run first.
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### Register tactics with `try?`. Tactics with larger priority run first.
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-/
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section Try

Mathlib/Tactic/Linter/EmptyLine.lean

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namespace Syntax
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/-!
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# `Syntax` filters
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### `Syntax` filters
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-/
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/--

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