Nuprl Lemma : partial_subtype_base
∀T:Type. ((T ⊆r Base) ⇒ (partial(T) ⊆r Base))
Proof
Definitions occuring in Statement :
partial: partial(T),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
base: Base,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
subtype_partial_sqtype_base,
subtype_rel_wf,
base_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
Error :universeIsType,
isectElimination,
instantiate,
universeEquality
Latex:
\mforall{}T:Type. ((T \msubseteq{}r Base) {}\mRightarrow{} (partial(T) \msubseteq{}r Base))
Date html generated:
2019_06_20-PM-00_33_50
Last ObjectModification:
2018_10_18-PM-02_46_33
Theory : partial_1
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