### Nuprl Lemma : equiv_rel_wf

`∀[T:Type]. ∀[E:T ⟶ T ⟶ ℙ].  (EquivRel(T;x,y.E[x;y]) ∈ ℙ)`

Proof

Definitions occuring in Statement :  equiv_rel: `EquivRel(T;x,y.E[x; y])` uall: `∀[x:A]. B[x]` prop: `ℙ` so_apply: `x[s1;s2]` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` equiv_rel: `EquivRel(T;x,y.E[x; y])` prop: `ℙ` and: `P ∧ Q` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]`
Lemmas referenced :  refl_wf sym_wf trans_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  introduction cut sqequalRule productEquality extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaEquality applyEquality hypothesis axiomEquality equalityTransitivity equalitySymmetry Error :functionIsType,  Error :universeIsType,  Error :inhabitedIsType,  universeEquality isect_memberEquality functionEquality cumulativity

Latex:
\mforall{}[T:Type].  \mforall{}[E:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    (EquivRel(T;x,y.E[x;y])  \mmember{}  \mBbbP{})

Date html generated: 2019_06_20-PM-00_28_49
Last ObjectModification: 2018_09_26-AM-11_46_36

Theory : rel_1

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