DefIsSetValued (3.28, Definition): “Is set-valued” predicate

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

Formula Display:

Proof Trees:

DefIsSetValued (3.28) — “Is set-valued” predicate

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

Num Entity Database Record (Vertical Field Table)

Title	“Is set-valued” predicate `#DefIsSetValued` `#label-is-set-valued-predicate`
Classification	Definition
Formula	0(∀(F:Class)((F set-valued )⟷(∀(x:Class)((x∈Dom(F))→(F(x) set ))))) 0\(\href{../symbols/delimiters-brackets.html}{(} \href{../symbols/forall-binder.html}{\forall} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{F} \href{../symbols/typing-colon.html}{:} \href{../symbols/class-type.html}{\mathsf{Class}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{F} \href{../symbols/set-valued-pred.html}{\mathsf{set\text{-}valued}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/iff-conn.html}{\longleftrightarrow} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/forall-binder.html}{\forall} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{x} \href{../symbols/typing-colon.html}{:} \href{../symbols/class-type.html}{\mathsf{Class}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{x} \href{../symbols/in-pred.html}{\in} \href{../symbols/dom-op.html}{\mathrm{Dom}} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{F} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/impl-conn.html}{\rightarrow} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{F} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{x} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/set-pred.html}{\mathsf{set}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \)
SML Kernel AST	`TpSetValued`
Scheme of Types	0`(∀([F@Variable]:[Class@Type])(([F@Class.Expression] set-valued)⟷(∀([x@Variable]:[Class@Type])(([x@Class.Expression]∈Dom([F@Class.Expression]))→([F@Class.Expression]([x@Class.Expression]) set)))))`
Verification	Definitional (Kernel AST) · Standalone Entry (`DefIsSetValued`) → · (3.28) · `#DefIsSetValued`