Nuprl Lemma : norm-snd_wf
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[N:⋂a:A. id-fun(B[a])]. (norm-snd(N) ∈ id-fun(a:A × B[a])) supposing ∀a:A. value-type(B[a])
Proof
Definitions occuring in Statement :
norm-snd: norm-snd(N),
id-fun: id-fun(T),
value-type: value-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
member: t ∈ T,
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
id-fun: id-fun(T),
norm-snd: norm-snd(N),
has-value: (a)↓,
so_apply: x[s],
prop: ℙ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
guard: {T},
all: ∀x:A. B[x],
implies: P ⇒ Q
Lemmas referenced :
value-type-has-value,
equal_wf,
set-value-type,
id-fun_wf,
all_wf,
value-type_wf,
set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
sqequalRule,
functionExtensionality,
productElimination,
thin,
callbyvalueReduce,
extract_by_obid,
isectElimination,
setEquality,
applyEquality,
hypothesisEquality,
cumulativity,
hypothesis,
independent_isectElimination,
lambdaEquality,
equalityTransitivity,
equalitySymmetry,
isectEquality,
functionEquality,
dependent_set_memberEquality,
dependent_pairEquality,
because_Cache,
setElimination,
rename,
productEquality,
axiomEquality,
isect_memberEquality,
universeEquality,
dependent_functionElimination,
lambdaFormation,
independent_functionElimination
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type].
\mforall{}[N:\mcap{}a:A. id-fun(B[a])]. (norm-snd(N) \mmember{} id-fun(a:A \mtimes{} B[a])) supposing \mforall{}a:A. value-type(B[a])
Date html generated:
2017_04_14-AM-07_22_08
Last ObjectModification:
2017_02_27-PM-02_55_15
Theory : call!by!value_2
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