RulForallInstantiation (2.02, Inference Rule): Forall Instantiation

RulForallInstantiation (2.02) — Forall Instantiation

First-order quantifier instantiation, abstraction rules, and non-empty discourse domain over Classes.

Num Entity Database Record (Vertical Field Table)

Title	Forall Instantiation `#RulForallInstantiation` `#label-forall-instantiation`
Classification	Inference Rule
Formula	0((∀(⦃x⦄:⟦X⟧)⟦𝛗⟧)→⟦𝛗[t/x]⟧) 0\(\href{../symbols/delimiters-brackets.html}{(} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/forall-binder.html}{\forall} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/binder-brackets.html}{\{\!\lvert } \href{../symbols/variables.html}{x} \href{../symbols/binder-brackets.html}{\rvert\!\}} \href{../symbols/typing-colon.html}{:} \href{../symbols/antiquotation.html}{[\![ } \href{../symbols/variables.html}{X} \href{../symbols/antiquotation.html}{ ]\!]} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/antiquotation.html}{[\![ } \href{../symbols/formula-metavariables.html}{\boldsymbol{\varphi}} \href{../symbols/antiquotation.html}{ ]\!]} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/impl-conn.html}{\rightarrow} \href{../symbols/antiquotation.html}{[\![ } \href{../symbols/formula-metavariables.html}{\boldsymbol{\varphi}} \href{../symbols/image-op.html}{[} \href{../symbols/variables.html}{t} \href{../symbols/subst-slash.html}{/} \href{../symbols/variables.html}{x} \href{../symbols/image-op.html}{]} \href{../symbols/antiquotation.html}{ ]\!]} \href{../symbols/delimiters-brackets.html}{)} \)
SML Kernel AST	`PForaL_prf`
Scheme of Types	0`((∀([⦃[x@Variable.Expression]⦄@Variable]:[⟦[X@Type.Expression.Expression]⟧@Type])⟦[𝛗@Fm.Expression]⟧)→⟦[𝛗@Fm.Expression][[t@LCEWIP]/[x@Variable.Expression]]⟧)`
Judgements	1[(t:X.Expression ), (X:Type ), (x:Name ), (𝛗:Fm )] 1\(\href{../symbols/image-op.html}{[} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{t} \href{../symbols/typing-colon.html}{:} \href{../symbols/variables.html}{X} \href{../symbols/dot-delim.html}{.} \href{../symbols/expression-sort.html}{\mathsf{Expression}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/comma-delim.html}{,} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{X} \href{../symbols/typing-colon.html}{:} \href{../symbols/type-sort.html}{\mathsf{Type}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/comma-delim.html}{,} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{x} \href{../symbols/typing-colon.html}{:} \href{../symbols/name-sort.html}{\mathsf{Name}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/comma-delim.html}{,} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/formula-metavariables.html}{\boldsymbol{\varphi}} \href{../symbols/typing-colon.html}{:} \href{../symbols/fm-sort.html}{\mathsf{Fm}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/image-op.html}{]} \)
Side Condition	1Fm .FFI ((t:X.Expression ),x,𝛗) 1\(\href{../symbols/fm-sort.html}{\mathsf{Fm}} \href{../symbols/dot-delim.html}{.} \href{../symbols/ffi-pred.html}{\mathrm{FFI}} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{t} \href{../symbols/typing-colon.html}{:} \href{../symbols/variables.html}{X} \href{../symbols/dot-delim.html}{.} \href{../symbols/expression-sort.html}{\mathsf{Expression}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/comma-delim.html}{,} \href{../symbols/variables.html}{x} \href{../symbols/comma-delim.html}{,} \href{../symbols/formula-metavariables.html}{\boldsymbol{\varphi}} \href{../symbols/delimiters-brackets.html}{)} \)
Verification	Primitive / Derived Rule (Kernel) · Standalone Entry (`RulForallInstantiation`) → · (2.02) · `#RulForallInstantiation`