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⊢

right tack

Right Tack

The turnstile ⊢ says a conclusion on the right can be proved from assumptions on the left. In logic it marks derivability; in typed programming it separates assumptions from a judgment about a term's type.

Text symbol
Also called
turnstile · tee · vdash
Search it as
proof rules · sequent · derivable · logic symbol · LaTeX vdash
Shows up in
Anything that takes text · its shape is whatever your font draws

What ⊢ means

It marks a conclusion proved from assumptions. In Γ ⊢ T, Γ (gamma) lists the assumptions and T is the conclusion. With nothing on the left, ⊢ T means T can be proved without listed assumptions.

The recognizable ancestor is the assertion sign used by the German logician Gottlob Frege in 1879. Gerhard Gentzen's work in 1934–35 helped develop notation for sequents: formal lines that set premises apart from conclusions.

Why does ⊢ change meaning with its neighbors?

The notation around it sets the relation. In proof theory, ⊢ marks derivability: a proof using a system's rules. In a sequent, formulas on the left are premises and formulas on the right are conclusions. In typed programming notation, it divides assumptions from a judgment that a term has a particular type.

Formal and technical: it signals proof notation in mathematical logic or typed programming.

Do not read ⊢ as a truth mark; ⊨ usually denotes semantic consequence.

What it means when someone sends it to you

3 readings
Γ ⊢ T
The assumptions in Γ prove T under the chosen system's rules.
⊢ T
T is derivable with no assumptions listed on the left.
Γ ⊢ t : A
With assumptions Γ, term t has type A.

Don't confuse it with

3
⊨
True
The double turnstile marks semantic consequence: every assignment that makes the premises true also makes the conclusion true.
⊣
Left Tack
The left tack has its vertical stroke at the opposite end; it is a separate, left-facing mark.
├
Box Drawings Light Vertical And Right
This is a box-drawing character. It may look similar, but it is not the logic turnstile.

Questions people ask

1

Can the assumptions before ⊢ be false?

Yes. Γ lists assumptions used in a derivation; ⊢ says what follows from them under the system's rules, not whether the assumptions are true.

How to type ⊢

Windows (Word)
Alt+XType 22A2, then Alt+X to get ⊢.
Windows
Win+Rrun charmap for the full table, or use the emoji picker's Ω symbols tab (Win + .).
macOS
Control+Command+SpaceOpen the character viewer and search “right tack”.
Linux
Ctrl+Shift+UType 22a2, then Enter or Space.
HTML
⊢
CSS
\22A2
how to type vdash in LaTeX
Use \vdash in math mode; it is available with an amssymb-compatible setup.
plain text
A plain-text `|-` can suggest the shape, but spacing and the chosen font affect the result.
Codes and encoding1 code points
HTML decimal
⊢
HTML hex
⊢
CSS content
content: "\22A2";
Each escape is closed by the next backslash; a trailing space is needed before a literal hex digit.
URL encoded
%E2%8A%A2
1
On screen
1
Code points
1
JS .length
3
UTF-8 bytes

A visible symbol can contain several code points. JS .length counts UTF-16 units; UTF-8 counts bytes.

Families this belongs to

1

Maths & numbers1,835 symbols

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