Nuprl Lemma : subtype_rel_set_simple
∀[A:Type]. ∀[P:A ⟶ ℙ]. ({a:A| P[a]} ⊆r A)
Proof
Definitions occuring in Statement :
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,
subtype_rel: A ⊆r B,
so_apply: x[s],
prop: ℙ
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
setElimination,
thin,
rename,
hypothesisEquality,
setEquality,
applyEquality,
hypothesis,
sqequalHypSubstitution,
sqequalRule,
universeEquality,
axiomEquality,
functionEquality,
cumulativity,
isect_memberEquality,
isectElimination,
because_Cache
Latex:
\mforall{}[A:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbP{}]. (\{a:A| P[a]\} \msubseteq{}r A)
Date html generated:
2016_05_13-PM-03_18_45
Last ObjectModification:
2015_12_26-AM-09_08_14
Theory : subtype_0
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