Nuprl Lemma : subtype_barSqtype_base
∀T:Type. ((T ⊆r Base) ⇒ (bar(T) ⊆r Base))
Proof
Definitions occuring in Statement :
bar: bar(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,
bar: bar(T),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
base_wf,
subtype_rel_wf,
subtype_partial_sqtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalRule,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
isectElimination,
universeEquality
Latex:
\mforall{}T:Type. ((T \msubseteq{}r Base) {}\mRightarrow{} (bar(T) \msubseteq{}r Base))
Date html generated:
2016_05_15-PM-10_03_48
Last ObjectModification:
2016_01_05-PM-06_24_37
Theory : bar!type
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