Nuprl Lemma : permr_equiv_rel
∀T:Type. EquivRel(T List;as,bs.as ≡(T) bs)
Proof
Definitions occuring in Statement :
permr: as ≡(T) bs,
list: T List,
equiv_rel: EquivRel(T;x,y.E[x; y]),
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
guard: {T},
implies: P ⇒ Q,
prop: ℙ,
equiv_rel: EquivRel(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y]),
sym: Sym(T;x,y.E[x; y]),
refl: Refl(T;x,y.E[x; y]),
and: P ∧ Q
Lemmas referenced :
list_wf,
permr_inversion,
permr_wf,
permr_transitivity,
permr_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
hypothesisEquality,
universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
dependent_functionElimination,
because_Cache,
independent_functionElimination,
inhabitedIsType,
universeEquality,
sqequalRule,
lambdaFormation_alt,
independent_pairFormation
Latex:
\mforall{}T:Type. EquivRel(T List;as,bs.as \mequiv{}(T) bs)
Date html generated:
2019_10_16-PM-01_00_30
Last ObjectModification:
2018_10_08-AM-11_54_22
Theory : perms_2
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