Nuprl Lemma : subtype_base_sq
∀[A:Type]. SQType(A) supposing A ⊆r Base
Proof
Definitions occuring in Statement :
sq_type: SQType(T),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
prop: ℙ,
guard: {T}
Lemmas referenced :
base_sq,
equal_wf,
base_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
lambdaFormation,
hypothesis,
dependent_functionElimination,
thin,
hypothesisEquality,
applyEquality,
sqequalRule,
independent_functionElimination,
because_Cache,
hyp_replacement,
equalitySymmetry,
applyLambdaEquality,
isectElimination,
cumulativity,
lambdaEquality,
sqequalAxiom,
isect_memberEquality,
equalityTransitivity,
universeEquality
Latex:
\mforall{}[A:Type]. SQType(A) supposing A \msubseteq{}r Base
Date html generated:
2017_04_14-AM-07_14_10
Last ObjectModification:
2017_02_27-PM-02_49_56
Theory : sqequal_1
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