Nuprl Lemma : approx-type_wf
∀[T:Type]. (approx-type(T) ∈ Type)
Proof
Definitions occuring in Statement :
approx-type: approx-type(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
guard: {T},
cand: A c∧ B,
and: P ∧ Q,
approx-per: approx-per(T;x;y),
prop: ℙ,
implies: P ⇒ Q,
all: ∀x:A. B[x],
uimplies: b supposing a,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
approx-type: approx-type(T),
member: t ∈ T,
uall: ∀[x:A]. B[x],
trans: Trans(T;x,y.E[x; y])
Lemmas referenced :
approx-per-trans,
base_wf,
approx-per_wf,
pertype_wf
Rules used in proof :
universeEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
because_Cache,
independent_pairFormation,
productElimination,
lambdaFormation,
independent_isectElimination,
hypothesis,
hypothesisEquality,
cumulativity,
lambdaEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]. (approx-type(T) \mmember{} Type)
Date html generated:
2018_05_21-PM-00_05_15
Last ObjectModification:
2017_12_30-PM-01_42_27
Theory : partial_1
Home
Index