Nuprl Lemma : subtype-approx-type
∀[T:Type]. T ⊆r approx-type(T) supposing mono(T) ∨ (T ⊆r Base)
Proof
Definitions occuring in Statement :
approx-type: approx-type(T),
mono: mono(T),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
or: P ∨ Q,
base: Base,
universe: Type
Definitions unfolded in proof :
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x y.t[x; y],
approx-type: approx-type(T),
all: ∀x:A. B[x],
or: P ∨ Q
Lemmas referenced :
base_wf,
subtype_rel_wf,
mono_wf,
or_wf,
approx-type_wf,
approx-per-for-base,
approx-per-for-mono
Rules used in proof :
universeEquality,
equalitySymmetry,
equalityTransitivity,
because_Cache,
isect_memberEquality,
cumulativity,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
hypothesis,
axiomEquality,
sqequalRule,
hypothesisEquality,
lambdaEquality,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
rename,
pertypeMemberEquality,
pointwiseFunctionalityForEquality,
dependent_functionElimination,
independent_isectElimination,
unionElimination
Latex:
\mforall{}[T:Type]. T \msubseteq{}r approx-type(T) supposing mono(T) \mvee{} (T \msubseteq{}r Base)
Date html generated:
2018_05_21-PM-00_05_19
Last ObjectModification:
2017_12_30-PM-02_20_37
Theory : partial_1
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