DefSetFunction (3.34, Definition): “Is a function” predicate

Standalone kernel entity record from 3. Set/Class-Theoretic Foundations (3.01–3.78) — View in Complete Entity Database (#DefSetFunction) →

Formula Display:
Proof Trees:

DefSetFunction (3.34) — “Is a function” predicate

Morse-Kelley / Von Neumann-Bernays-Gödel class comprehension, sethood, ordinals, Dunaev pairs, cardinals, universes, and reflection.

Num Entity Database Record (Vertical Field Table)
3.34
Title “Is a function” predicate #DefSetFunction #label-is-a-function-predicate
Classification Definition
Formula
0\(\href{../symbols/delimiters-brackets.html}{(} \href{../symbols/forall-binder.html}{\forall} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{f} \href{../symbols/typing-colon.html}{:} \href{../symbols/class-type.html}{\mathsf{Class}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{f} \href{../symbols/func-pred.html}{\mathsf{function}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/iff-conn.html}{\longleftrightarrow} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{f} \href{../symbols/class-func-pred.html}{\mathsf{class\text{-}function}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/and-conn.html}{\land} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{f} \href{../symbols/set-pred.html}{\mathsf{set}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \)
SML Kernel AST TpFunc
Scheme of Types 0(∀([f@Variable]:[Class@Type])(([f@Class.Expression] function)⟷(([f@Class.Expression] class-function)∧([f@Class.Expression] set))))
Verification Definitional (Kernel AST) · Standalone Entry (DefSetFunction) → · (3.34) · #DefSetFunction