Markdown mathematical proof template: a claim in plain prose

A Markdown mathematical proof template puts a single claim beside the premises that support it. The argument then connects those premises to the conclusion through justified sentences. Here that means a short proof about invented tiles, written entirely in ordinary words.

Everything about the tiles is stipulated inside the example. The argument establishes its claim within those premises alone; nothing here asserts a result about real mathematics or anyone else's writing.

What the proof file contains

The claim sentence says exactly what the argument establishes. Definitions fix the meaning of its nouns. Named premises state the facts taken as given. The proof paragraphs draw on those facts, referring back whenever an earlier deduction supplies part of a later one. The final sentence returns to the original claim.

A premise is an assumption for this invented setting, not a fact established by the proof. Keeping that distinction visible matters when a sentence sounds plausible but has no stated basis. Blue tiles need no particular texture here, for example, because no premise gives them one.

For the extension's meaning, consult the .md explanation. For this post, the file holds the claim and its argument as writing, with no calculation notation needed.

The proof template with invented tiles

Fictional writer Jane Doe devises this argument for the fictional Doe project. She invents a collection of tiles and a pouch drawn from that collection. Neither the tiles nor the project refers to anything outside this example.

Copy the block as a reusable shape. A bracketed title awaits replacement above the finished claim, definitions, premises and proof. For another invented claim, replace those parts together so each deduction still follows from the premises stated in that file.

# [proof title]

Every tile in the Doe pouch is blue.

## Definitions and premises

Jane Doe uses Doe collection to mean an invented collection of tiles. Doe pouch means a pouch whose tiles belong to that collection. Rough is a texture description; not rough excludes that description.

Color premise: Every tile in the Doe collection is either blue or gold, and no tile is both colors.

Texture premise: Every gold tile in the Doe collection is rough.

Pouch premise: Every tile in the Doe pouch belongs to the Doe collection and is not rough.

## Proof

First step: Consider any tile in the Doe pouch. By the Pouch premise, this tile belongs to the Doe collection and is not rough.

Second step: By the collection membership established in the first step and the Color premise, this tile is either blue or gold.

Third step: If this tile were gold, the Texture premise would make it rough. The first step establishes that it is not rough, so this tile cannot be gold.

Fourth step: The second step restricts this tile's color to blue or gold. The third step excludes gold, so this tile is blue.

The tile considered was any tile in the Doe pouch, so every tile in the Doe pouch is blue, as claimed.

The proof uses a tile chosen without any extra description. That choice lets the final sentence apply to every pouch tile. Nothing in the argument depends on a particular tile's size or position, or on the number of tiles the pouch holds.

Gold is excluded through the texture sentences. The argument does not assume that every blue tile is not rough. It needs only the given fact that pouch tiles are not rough and the given fact that gold tiles are rough.

The example sits in a fence tagged text. Fence delimiters have their own explanation in Markdown code block notation; the paragraphs inside this block carry the argument.

Keeping each step traceable

Read each deduction beside the sentence it names. The second step needs collection membership from the first step before the Color premise applies. The third step needs both the Texture premise and the first step's exclusion of roughness. The fourth step joins the remaining color choice to the exclusion of gold.

A missing connection calls for a sentence explaining the inference. A new assumption belongs before the proof, among its premises. Changing a premise can change what follows from it, so the conclusion has to stay within the stated assumptions. Repeating the claim at the end closes that chain without adding another claim.

Naming the proof file

Naming this example doe-pouch-blue-proof.md places its subject and conclusion together. Keep the title specific to that same claim. File punctuation and word separators are covered by Markdown naming conventions.

The reusable part is the arrangement: claim, definitions, premises, argument and conclusion. The colors and pouch belong to this example. A different invented collection needs its own stated assumptions rather than an unexplained carryover from these tiles.

Where Sashmark fits

A proof's sentences offer something to read and revise. Sashmark would pair planned Markdown editing with desktop reading for people receiving agent-written files. Both roles belong to Sashmark's app in development.