Nuprl Lemma : non-void-decl-single
∀[T,A:Type]. ∀x:T. ∀eq:EqDecider(T). (A ⇒ non-void(x : A))
Proof
Definitions occuring in Statement :
non-void-decl: non-void(d),
fpf-single: x : v,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
non-void-decl: non-void(d),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
prop: ℙ,
so_apply: x[s1;s2],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
fpf-all-single-decl,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
dependent_functionElimination,
hypothesisEquality,
lambdaEquality,
universeEquality,
productElimination,
independent_functionElimination,
hypothesis
Latex:
\mforall{}[T,A:Type]. \mforall{}x:T. \mforall{}eq:EqDecider(T). (A {}\mRightarrow{} non-void(x : A))
Date html generated:
2018_05_21-PM-09_30_26
Last ObjectModification:
2018_02_09-AM-10_24_57
Theory : finite!partial!functions
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