-
universal quantifier is
encoded as U+2200 ∀ FOR ALL in Unicode, and as \
forall in
LaTeX and
related formula editors.
Suppose it is
given that 2·0 = 0 +...
- ( x , y ) = 0 ) ] {\displaystyle (\
forall x\
forall y\,[\mathop {\leq } (\mathop {+} (x,y),z)\to \
forall x\,\
forall y\,\mathop {+} (x,y)=0)]} is a formula...
- (quantified) type variables. E.g.: cons :
forall a . a -> List a -> List a nil :
forall a . List a id :
forall a . a -> a
Polymorphic types can become...
- {\displaystyle \
forall A\
forall w_{1}\
forall w_{2}\ldots \
forall w_{n}{\bigl [}\
forall x(x\in A\Rightarrow \exists !y\,\varphi )\Rightarrow \exists B\ \
forall x{\bigl...
- < δ ⟹ | f ( x ) − L | < ε ) . {\displaystyle (\
forall \varepsilon >0)\,(\exists \delta >0)\,(\
forall x\in \mathbb {R} )\,(|x-p|<\delta \implies |f(x)-L|<\varepsilon...
-
closures (as in ∀ v 0 . ∀ v 1 . ⋯ ∀ v n . {\displaystyle \
forall v_{0}.\
forall v_{1}.\cdots \
forall v_{n}.} ).
Basic constructive set
theory B C S T {\displaystyle...
- {\displaystyle \
forall x_{1}\ldots \
forall x_{n}\;\exists y\;P(y)} with ∀ x 1 … ∀ x n P ( f ( x 1 , … , x n ) ) {\displaystyle \
forall x_{1}\ldots \
forall x_{n}\;P(f(x_{1}...
- {\begin{aligned}\
forall x,p(x)\to (\
forall y,q(x)\to \pm r(x,y)),&\quad \
forall x,p(x)\to (\exists y,q(x)\wedge \pm r(x,y))\\\exists x,p(x)\wedge (\
forall y,q(x)\to...
- \vdash \!P(x)} has been derived, then ⊢ ∀ x P ( x ) {\displaystyle \vdash \!\
forall x\,P(x)} can be derived. The full
generalization rule
allows for hypotheses...
-
universal quantifier ∀ {\displaystyle \
forall } in the first-order
formula ∀ x P ( x ) {\displaystyle \
forall xP(x)}
expresses that
everything in the...
