Nuprl Lemma : b_all-wf2
∀[T:Type]. ∀[b:bag(T)]. ∀[P:{x:T| x ↓∈ b} ⟶ ℙ]. (b_all(T;b;x.P[x]) ∈ ℙ)
Proof
Definitions occuring in Statement :
b_all: b_all(T;b;x.P[x]),
bag-member: x ↓∈ bs,
bag: bag(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
b_all: b_all(T;b;x.P[x]),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
subtype_rel: A ⊆r B
Lemmas referenced :
all_wf,
bag-member_wf,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
lambdaEquality,
functionEquality,
because_Cache,
hypothesis,
applyEquality,
dependent_set_memberEquality,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
setEquality,
isect_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[b:bag(T)]. \mforall{}[P:\{x:T| x \mdownarrow{}\mmember{} b\} {}\mrightarrow{} \mBbbP{}]. (b\_all(T;b;x.P[x]) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-02_41_15
Last ObjectModification:
2015_12_27-AM-09_40_50
Theory : bags
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