Nuprl Lemma : alpha-eq-terms_weakening
∀[opr:Type]. ∀a,b:term(opr). ((a = b ∈ term(opr)) ⇒ alpha-eq-terms(opr;b;a))
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,
equal: s = t ∈ T
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,
guard: {T},
refl: Refl(T;x,y.E[x; y]),
prop: ℙ
Lemmas referenced :
alpha-eq-equiv-rel,
term_wf,
istype-universe,
alpha-eq-terms_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productElimination,
lambdaFormation_alt,
equalityIstype,
inhabitedIsType,
universeIsType,
instantiate,
universeEquality,
dependent_functionElimination,
hyp_replacement,
equalitySymmetry,
sqequalRule,
dependent_set_memberEquality_alt,
independent_pairFormation,
equalityTransitivity,
productIsType,
applyLambdaEquality,
setElimination,
rename
Latex:
\mforall{}[opr:Type]. \mforall{}a,b:term(opr). ((a = b) {}\mRightarrow{} alpha-eq-terms(opr;b;a))
Date html generated:
2020_05_19-PM-09_55_44
Last ObjectModification:
2020_03_09-PM-04_09_03
Theory : terms
Home
Index