Nuprl Lemma : alpha-eq-terms_transitivity
∀[opr:Type]. ∀a,b,c:term(opr).  (alpha-eq-terms(opr;a;b) 
⇒ alpha-eq-terms(opr;b;c) 
⇒ alpha-eq-terms(opr;a;c))
Proof
Definitions occuring in Statement : 
alpha-eq-terms: alpha-eq-terms(opr;a;b)
, 
term: term(opr)
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
equiv_rel: EquivRel(T;x,y.E[x; y])
, 
and: P ∧ Q
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
guard: {T}
, 
trans: Trans(T;x,y.E[x; y])
Lemmas referenced : 
alpha-eq-equiv-rel, 
alpha-eq-terms_wf, 
term_wf, 
istype-universe
Rules used in proof : 
cut, 
introduction, 
extract_by_obid, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
hypothesis, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
productElimination, 
lambdaFormation_alt, 
universeIsType, 
inhabitedIsType, 
instantiate, 
universeEquality, 
dependent_functionElimination, 
independent_functionElimination
Latex:
\mforall{}[opr:Type]
    \mforall{}a,b,c:term(opr).    (alpha-eq-terms(opr;a;b)  {}\mRightarrow{}  alpha-eq-terms(opr;b;c)  {}\mRightarrow{}  alpha-eq-terms(opr;a;c))
Date html generated:
2020_05_19-PM-09_55_41
Last ObjectModification:
2020_03_09-PM-04_09_01
Theory : terms
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