Nuprl Lemma : decidable-equal-deq
∀[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],
implies: P ⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T
Lemmas referenced :
deq_wf,
deq-witness_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
rename,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
universeEquality,
introduction
Latex:
\mforall{}[T:Type]. (EqDecider(T) {}\mRightarrow{} (\mforall{}x,y:T. Dec(x = y)))
Date html generated:
2016_05_14-AM-06_06_40
Last ObjectModification:
2015_12_26-AM-11_46_40
Theory : equality!deciders
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