Nuprl Lemma : deq-exists
∀[T:Type]. (EqDecider(T) ⇐⇒ ∀x,y:T. Dec(x = y ∈ T))
Proof
Definitions occuring in Statement :
deq: EqDecider(T),
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
rev_implies: P ⇐ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
deq_wf,
all_wf,
decidable_wf,
equal_wf,
deq-witness_wf,
mk_deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
independent_pairFormation,
lambdaFormation,
rename,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
universeEquality,
introduction
Latex:
\mforall{}[T:Type]. (EqDecider(T) \mLeftarrow{}{}\mRightarrow{} \mforall{}x,y:T. Dec(x = y))
Date html generated:
2016_05_14-AM-06_06_42
Last ObjectModification:
2015_12_26-AM-11_46_41
Theory : equality!deciders
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