DefUnaryUnion (3.19, Definition): Union of the elements of a class

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

Formula Display:
Proof Trees:

DefUnaryUnion (3.19) — Union of the elements of a class

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

Num Entity Database Record (Vertical Field Table)
3.19
Title Union of the elements of a class #DefUnaryUnion #label-union-of-the-elements-of-a-class
Classification Definition
Formula
0\(\href{../symbols/delimiters-brackets.html}{(} \href{../symbols/forall-binder.html}{\forall} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{K} \href{../symbols/typing-colon.html}{:} \href{../symbols/class-type.html}{\mathsf{Class}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/bigunion-op.html}{\bigcup} \href{../symbols/variables.html}{K} \href{../symbols/eq-pred.html}{=} \href{../symbols/class-comprehension.html}{\{} \href{../symbols/variables.html}{x} \href{../symbols/class-comprehension.html}{ \mid } \href{../symbols/exists-binder.html}{\exists} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{y} \href{../symbols/typing-colon.html}{:} \href{../symbols/class-type.html}{\mathsf{Class}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{y} \href{../symbols/in-pred.html}{\in} \href{../symbols/variables.html}{K} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/and-conn.html}{\land} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{x} \href{../symbols/in-pred.html}{\in} \href{../symbols/variables.html}{y} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/class-comprehension.html}{\}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \)
SML Kernel AST CpUnion
Scheme of Types 0(∀([K@Variable]:[Class@Type])(⋃[K@Class.Expression]={[x@Class.Expression]|∃([y@Variable]:[Class@Type])(([y@Class.Expression]∈[K@Class.Expression])∧([x@Class.Expression]∈[y@Class.Expression]))}))
Verification Definitional (Kernel AST) · Standalone Entry (DefUnaryUnion) → · (3.19) · #DefUnaryUnion