DefTightClass (3.47, Definition): “Is tight” predicate

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

Formula Display:
Proof Trees:

DefTightClass (3.47) — “Is tight” predicate

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

Num Entity Database Record (Vertical Field Table)
3.47
Title “Is tight” predicate #DefTightClass #label-is-tight-predicate
Classification Definition
Formula
0\(\href{../symbols/delimiters-brackets.html}{(} \href{../symbols/forall-binder.html}{\forall} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{U} \href{../symbols/typing-colon.html}{:} \href{../symbols/class-type.html}{\mathsf{Class}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/tight-pred.html}{\mathsf{Tight}} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{U} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/iff-conn.html}{\longleftrightarrow} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/forall-binder.html}{\forall} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{B} \href{../symbols/typing-colon.html}{:} \href{../symbols/class-type.html}{\mathsf{Class}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{B} \href{../symbols/sub-pred.html}{\subseteq} \href{../symbols/variables.html}{U} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/impl-conn.html}{\rightarrow} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{B} \href{../symbols/card-lt-pred.html}{\prec} \href{../symbols/variables.html}{U} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/iff-conn.html}{\longleftrightarrow} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{B} \href{../symbols/in-pred.html}{\in} \href{../symbols/variables.html}{U} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \)
SML Kernel AST PKernelDef_prf
Scheme of Types 0(∀([U@Variable]:[Class@Type])(Tight([U@Class.Expression])⟷(∀([B@Variable]:[Class@Type])(([B@Class.Expression]⊆[U@Class.Expression])→(([B@Class.Expression]≺[U@Class.Expression])⟷([B@Class.Expression]∈[U@Class.Expression]))))))
Verification Definitional (Kernel AST) · Standalone Entry (DefTightClass) → · (3.47) · #DefTightClass