TeXipedia

Lleftarrow

Represents a strong leftward relationship or multi-step implication in mathematical logic and formal reasoning.

Overview

Serves as an enhanced leftward arrow notation in formal mathematics and theoretical computer science, indicating relationships that are more structured or significant than simple implications.

  • Common in category theory to denote special types of morphisms or functors
  • Used in formal logic to show complex dependencies or transformations
  • Appears in theoretical computer science for expressing program transformations or state transitions
  • Helpful in mathematical proofs where multiple steps or conditions lead to a conclusion

Examples

Showing a strong logical implication or consequence in reverse direction

B⇚Ameans A strongly implies BB \Lleftarrow A \quad \text{means A strongly implies B} 
B \Lleftarrow A \quad \text{means A strongly implies B}

Indicating a multi-step transformation or reduction between mathematical expressions

x2+2x+1⇚(x+1)2x^2 + 2x + 1 \Lleftarrow (x+1)^2 
x^2 + 2x + 1 \Lleftarrow (x+1)^2

Representing a functional dependency in database theory or set relations

{Name, Age}⇚{ID}\{\text{Name, Age}\} \Lleftarrow \{\text{ID}\} 
\{\text{Name, Age}\} \Lleftarrow \{\text{ID}\}