Nuprl Lemma : bag-admissable_wf
∀[T:Type]. ∀[R:bag(T) ⟶ bag(T) ⟶ ℙ]. (bag-admissable(T;as,bs.R[as;bs]) ∈ ℙ)
Proof
Definitions occuring in Statement :
bag-admissable: bag-admissable(T;as,bs.R[as; bs]),
bag: bag(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag-admissable: bag-admissable(T;as,bs.R[as; bs]),
prop: ℙ,
and: P ∧ Q,
so_lambda: λ2x.t[x],
so_apply: x[s1;s2],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B
Lemmas referenced :
all_wf,
bag_wf,
empty-bag_wf,
bag-append_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
productEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
lambdaEquality,
applyEquality,
because_Cache,
functionEquality,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[R:bag(T) {}\mrightarrow{} bag(T) {}\mrightarrow{} \mBbbP{}]. (bag-admissable(T;as,bs.R[as;bs]) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-03_10_33
Last ObjectModification:
2015_12_27-AM-09_25_16
Theory : bags
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