DefClassFunction (3.32, Definition): “Is a class-function” predicate

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

Formula Display:
Proof Trees:

DefClassFunction (3.32) — “Is a class-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)
3.32
Title “Is a class-function” predicate #DefClassFunction #label-is-a-class-function-predicate
Classification Definition
Formula
0\(\href{../symbols/delimiters-brackets.html}{(} \href{../symbols/forall-binder.html}{\forall} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{F} \href{../symbols/typing-colon.html}{:} \href{../symbols/class-type.html}{\mathsf{Class}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{F} \href{../symbols/class-func-pred.html}{\mathsf{class\text{-}function}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/iff-conn.html}{\longleftrightarrow} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{F} \href{../symbols/family-pred.html}{\mathsf{family}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/and-conn.html}{\land} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{F} \href{../symbols/set-valued-pred.html}{\mathsf{set\text{-}valued}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \)
SML Kernel AST TpClassFunc
Scheme of Types 0(∀([F@Variable]:[Class@Type])(([F@Class.Expression] class-function)⟷(([F@Class.Expression] family)∧([F@Class.Expression] set-valued))))
Verification Definitional (Kernel AST) · Standalone Entry (DefClassFunction) → · (3.32) · #DefClassFunction