Nuprl Lemma : deq_subtype
∀[T:Type]. (EqDecider(T) ⊆r (T ⟶ T ⟶ 𝔹))
Proof
Definitions occuring in Statement :
deq: EqDecider(T),
bool: 𝔹,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
deq: EqDecider(T)
Lemmas referenced :
bool_wf,
deq_wf
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lemma_by_obid,
hypothesis,
isect_memberFormation,
introduction,
lambdaEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
hypothesisEquality,
isectElimination,
sqequalRule,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. (EqDecider(T) \msubseteq{}r (T {}\mrightarrow{} T {}\mrightarrow{} \mBbbB{}))
Date html generated:
2016_05_14-AM-06_06_16
Last ObjectModification:
2015_12_26-AM-11_46_48
Theory : equality!deciders
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