Nuprl Lemma : alpha-eq-terms_functionality
∀[opr:Type]
∀x1,x2,y1,y2:term(opr).
(alpha-eq-terms(opr;x1;x2)
⇒ alpha-eq-terms(opr;y1;y2)
⇒ (alpha-eq-terms(opr;x1;y1) ⇐⇒ alpha-eq-terms(opr;x2;y2)))
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],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
member: t ∈ T,
guard: {T},
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
alpha-eq-terms_inversion,
alpha-eq-terms_transitivity,
alpha-eq-terms_wf,
term_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation_alt,
independent_pairFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
independent_functionElimination,
hypothesis,
universeIsType,
inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}[opr:Type]
\mforall{}x1,x2,y1,y2:term(opr).
(alpha-eq-terms(opr;x1;x2)
{}\mRightarrow{} alpha-eq-terms(opr;y1;y2)
{}\mRightarrow{} (alpha-eq-terms(opr;x1;y1) \mLeftarrow{}{}\mRightarrow{} alpha-eq-terms(opr;x2;y2)))
Date html generated:
2020_05_19-PM-09_55_46
Last ObjectModification:
2020_03_09-PM-04_09_07
Theory : terms
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