Nuprl Lemma : all-value-type
∀[A:Type]. ∀[a:A]. ∀[B:A ⟶ Type]. value-type(∀a:A. B[a]) supposing value-type(B[a])
Proof
Definitions occuring in Statement :
value-type: value-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
squash: ↓T,
all: ∀x:A. B[x],
value-type: value-type(T),
has-value: (a)↓
Lemmas referenced :
function-value-type,
value-type_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
Error :lambdaEquality_alt,
applyEquality,
Error :inhabitedIsType,
independent_isectElimination,
Error :dependent_pairFormation_alt,
hypothesis,
Error :universeIsType,
imageMemberEquality,
baseClosed,
Error :isect_memberEquality_alt,
axiomSqleEquality,
Error :isectIsTypeImplies,
Error :functionIsType,
instantiate,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[a:A]. \mforall{}[B:A {}\mrightarrow{} Type]. value-type(\mforall{}a:A. B[a]) supposing value-type(B[a])
Date html generated:
2019_06_20-AM-11_21_30
Last ObjectModification:
2019_01_28-PM-03_33_44
Theory : call!by!value_1
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