Nuprl Lemma : p_equiv_wf

∀[T:Type]. ∀[A,B:T ⟶ ℙ].  (A ≡{T} B ∈ ℙ)


Proof




Definitions occuring in Statement :  p_equiv: A ≡{T} B,  uall: ∀[x:A]. B[x],  prop: ℙ,  member: t ∈ T,  function: x:A ⟶ B[x],  universe: Type
Definitions unfolded in proof :  p_equiv: A ≡{T} B,  uall: ∀[x:A]. B[x],  member: t ∈ T,  prop: ℙ
Lemmas referenced :  and_wf,  p_subset_wf
Rules used in proof :  sqequalSubstitution,  sqequalRule,  sqequalReflexivity,  sqequalTransitivity,  computationStep,  isect_memberFormation,  introduction,  cut,  lemma_by_obid,  sqequalHypSubstitution,  isectElimination,  thin,  hypothesisEquality,  hypothesis,  axiomEquality,  equalityTransitivity,  equalitySymmetry,  functionEquality,  cumulativity,  universeEquality,  isect_memberEquality,  because_Cache

Latex:
\mforall{}[T:Type].  \mforall{}[A,B:T  {}\mrightarrow{}  \mBbbP{}].    (A  \mequiv{}\{T\}  B  \mmember{}  \mBbbP{})



Date html generated: 2016_05_15-PM-00_00_18
Last ObjectModification: 2015_12_26-PM-11_26_52

Theory : gen_algebra_1


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