DefValueAtArg (3.25, Definition): Evaluation of a [function|class-function|family]

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

Formula Display:
Proof Trees:

DefValueAtArg (3.25) — Evaluation of a [function|class-function|family]

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

Num Entity Database Record (Vertical Field Table)
3.25
Title Evaluation of a [function|class-function|family] #DefValueAtArg #label-evaluation-of-a-function-class-function-family
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/forall-binder.html}{\forall} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{a} \href{../symbols/typing-colon.html}{:} \href{../symbols/class-type.html}{\mathsf{Class}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{F} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{a} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/eq-pred.html}{=} \href{../symbols/antiquotation.html}{[\![ } \href{../symbols/class-if-then-else.html}{\mathbf{IF}} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/exists-binder.html}{\exists} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{s} \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}{a} \href{../symbols/comma-delim.html}{,} \href{../symbols/variables.html}{s} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/in-pred.html}{\in} \href{../symbols/variables.html}{F} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/class-if-then-else.html}{\mathbf{THEN}} \href{../symbols/bigunion-op.html}{\bigcup} \href{../symbols/class-comprehension.html}{\{} \href{../symbols/variables.html}{s} \href{../symbols/class-comprehension.html}{ \mid } \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{a} \href{../symbols/comma-delim.html}{,} \href{../symbols/variables.html}{s} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/in-pred.html}{\in} \href{../symbols/variables.html}{F} \href{../symbols/class-comprehension.html}{\}} \href{../symbols/class-if-then-else.html}{\mathbf{ELSE}} \href{../symbols/universal-class-const.html}{\mathbf{V}} \href{../symbols/class-if-then-else.html}{\mathbf{FI}} \href{../symbols/antiquotation.html}{ ]\!]} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \)
SML Kernel AST CpValOf
Scheme of Types 0(∀([F@Variable]:[Class@Type])∀([a@Variable]:[Class@Type])([F@Class.Expression]([a@Class.Expression])=⟦IF (∃([s@Variable]:[Class@Type])(([a@Class.Expression],[s@Class.Expression])∈[F@Class.Expression])) THEN ⋃{[s@Class.Expression]|([a@Class.Expression],[s@Class.Expression])∈[F@Class.Expression]} ELSE V FI⟧))
Verification Definitional (Kernel AST) · Standalone Entry (DefValueAtArg) → · (3.25) · #DefValueAtArg