Nuprl Lemma : cbv-all-identity
∀[T:Type]. ∀[t:T]. let x ⟵ t in x ∈ T supposing valueall-type(T)
Proof
Definitions occuring in Statement :
valueall-type: valueall-type(T),
callbyvalueall: callbyvalueall,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a)
Lemmas referenced :
valueall-type-has-valueall,
evalall-reduce,
valueall-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
callbyvalueReduce,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[t:T]. let x \mleftarrow{}{} t in x \mmember{} T supposing valueall-type(T)
Date html generated:
2016_05_13-PM-04_07_53
Last ObjectModification:
2015_12_26-AM-11_03_41
Theory : fun_1
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