Nuprl Lemma : subtype_rel_set
∀[A,B:Type]. ∀[P:A ⟶ ℙ]. {a:A| P[a]} ⊆r B supposing A ⊆r B
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
so_apply: x[s],
prop: ℙ
Lemmas referenced :
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
setElimination,
thin,
rename,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalHypSubstitution,
sqequalRule,
setEquality,
because_Cache,
axiomEquality,
lemma_by_obid,
isectElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbP{}]. \{a:A| P[a]\} \msubseteq{}r B supposing A \msubseteq{}r B
Date html generated:
2016_05_13-PM-03_18_45
Last ObjectModification:
2015_12_26-AM-09_08_20
Theory : subtype_0
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