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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