Nuprl Lemma : very-dep-fun_wf
∀[A,B:Type]. ∀[C:A ⟶ B ⟶ Type]. (very-dep-fun(A;B;a,b.C[a;b]) ∈ Type)
Proof
Definitions occuring in Statement :
very-dep-fun: very-dep-fun(A;B;a,b.C[a; b]),
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
very-dep-fun: very-dep-fun(A;B;a,b.C[a; b]),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
vdf_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
isectEquality,
intEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality_alt,
applyEquality,
universeIsType,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionIsType,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
instantiate,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[C:A {}\mrightarrow{} B {}\mrightarrow{} Type]. (very-dep-fun(A;B;a,b.C[a;b]) \mmember{} Type)
Date html generated:
2020_05_19-PM-09_40_22
Last ObjectModification:
2020_03_05-AM-11_15_14
Theory : co-recursion-2
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