Nuprl Lemma : subtype-value-type
∀[A,B:Type]. (value-type(A)) supposing (value-type(B) and (A ⊆r B))
Proof
Definitions occuring in Statement :
value-type: value-type(T),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
value-type: value-type(T),
sq_stable: SqStable(P),
implies: P ⇒ Q,
all: ∀x:A. B[x],
has-value: (a)↓,
subtype_rel: A ⊆r B,
prop: ℙ,
squash: ↓T
Lemmas referenced :
sq_stable__has-value,
value-type-has-value,
equal_wf,
equal-wf-base,
base_wf,
value-type_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
applyEquality,
sqequalRule,
independent_isectElimination,
dependent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
because_Cache,
isect_memberEquality,
axiomSqleEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[A,B:Type]. (value-type(A)) supposing (value-type(B) and (A \msubseteq{}r B))
Date html generated:
2017_04_14-AM-07_15_47
Last ObjectModification:
2017_02_27-PM-02_51_00
Theory : call!by!value_1
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