Nuprl Lemma : evalall-reduce
∀[T:Type]. ∀[t:T]. evalall(t) ~ t supposing valueall-type(T)
Proof
Definitions occuring in Statement :
valueall-type: valueall-type(T),
evalall: evalall(t),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
valueall-type: valueall-type(T),
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
squash: ↓T
Lemmas referenced :
evalall-sqequal,
valueall-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
pointwiseFunctionality,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
equalityTransitivity,
equalitySymmetry,
because_Cache,
sqequalRule,
sqequalExtensionalEquality,
independent_pairFormation,
Error :lambdaFormation_alt,
Error :universeIsType,
sqequalIntensionalEquality,
imageMemberEquality,
baseClosed,
axiomSqEquality,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
Error :inhabitedIsType,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[t:T]. evalall(t) \msim{} t supposing valueall-type(T)
Date html generated:
2019_06_20-PM-00_26_50
Last ObjectModification:
2018_10_15-PM-00_48_54
Theory : fun_1
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