-
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 +...
- {\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...
- ( 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...
- {\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}...
- (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...
- < δ ⟹ | f ( x ) − L | < ε ) . {\displaystyle (\
forall \varepsilon >0)\,(\exists \delta >0)\,(\
forall x\in \mathbb {R} )\,(0<|x-p|<\delta \implies |f(x)-L|<\varepsilon...
- {\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...
- x ∃ y ∀ z ( ϕ ( y ) ∨ ( ψ ( z ) → ρ ( x ) ) ) {\displaystyle \
forall x\exists y\
forall z(\phi (y)\lor (\psi (z)\rightarrow \rho (x)))} is in
prenex normal...
- \
forall x\ (x+0=x)} ∀ x , y ( x + S ( y ) = S ( x + y ) ) {\displaystyle \
forall x,y\ (x+S(y)=S(x+y))} ∀ x ( x ⋅ 0 = 0 ) {\displaystyle \
forall x\...
- \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...
