Nuprl Lemma : alpha-eq-equiv-rel
∀[opr:Type]. EquivRel(term(opr);a,b.alpha-eq-terms(opr;a;b))
Proof
Definitions occuring in Statement : 
alpha-eq-terms: alpha-eq-terms(opr;a;b)
, 
term: term(opr)
, 
equiv_rel: EquivRel(T;x,y.E[x; y])
, 
uall: ∀[x:A]. B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
equiv_rel: EquivRel(T;x,y.E[x; y])
, 
and: P ∧ Q
, 
refl: Refl(T;x,y.E[x; y])
, 
all: ∀x:A. B[x]
, 
alpha-eq-terms: alpha-eq-terms(opr;a;b)
, 
member: t ∈ T
, 
cand: A c∧ B
, 
sym: Sym(T;x,y.E[x; y])
, 
implies: P 
⇒ Q
, 
iff: P 
⇐⇒ Q
, 
prop: ℙ
, 
trans: Trans(T;x,y.E[x; y])
Lemmas referenced : 
alpha-aux-refl, 
nil_wf, 
varname_wf, 
term_wf, 
alpha-aux-symm, 
alpha-eq-terms_wf, 
istype-universe, 
alpha-aux-trans
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
independent_pairFormation, 
lambdaFormation_alt, 
cut, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
dependent_functionElimination, 
hypothesis, 
universeIsType, 
because_Cache, 
productElimination, 
independent_functionElimination, 
sqequalRule, 
instantiate, 
universeEquality
Latex:
\mforall{}[opr:Type].  EquivRel(term(opr);a,b.alpha-eq-terms(opr;a;b))
Date html generated:
2020_05_19-PM-09_55_39
Last ObjectModification:
2020_03_09-PM-04_09_00
Theory : terms
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