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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