TeXipedia

Rrightarrow

Represents a strong or multi-step logical implication, transformation, or derivation in mathematical proofs and formal systems.

Overview

Commonly employed in advanced mathematical contexts where standard implications are insufficient to capture complex relationships or transformations.

  • Essential in category theory for depicting special types of morphisms or functorial relationships
  • Used in formal logic to denote higher-order implications or multi-step derivations
  • Appears in proof theory to show complex transformational steps or strong logical consequences
  • Valuable in abstract algebra and theoretical computer science for expressing sophisticated mathematical structures

Examples

Showing a multi-step logical deduction or strong implication in mathematical logic.

P∧Q⇛RP \land Q \Rrightarrow R 
P \land Q \Rrightarrow R

Representing a complex transformation or multi-step derivation in category theory.

A→fB→gC⇛DA \xrightarrow{f} B \xrightarrow{g} C \Rrightarrow D 
A \xrightarrow{f} B \xrightarrow{g} C \Rrightarrow D

Indicating a strong consequence or conclusion in formal systems.

(∀x)(P(x)∧Q(x))⇛(∀x)(R(x))(\forall x)(P(x) \land Q(x)) \Rrightarrow (\forall x)(R(x)) 
(\forall x)(P(x) \land Q(x)) \Rrightarrow (\forall x)(R(x))