Nuprl Lemma : bfs-predicate_wf
∀[K:RngSig]. ∀[S:Type]. ∀[P:(|K| × S) ⟶ ℙ]. ∀[b:basic-formal-sum(K;S)]. (bfs-predicate(K;S;p.P[p];b) ∈ ℙ)
Proof
Definitions occuring in Statement :
bfs-predicate: bfs-predicate(K;S;p.P[p];b),
basic-formal-sum: basic-formal-sum(K;S),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type,
rng_car: |r|,
rng_sig: RngSig
Definitions unfolded in proof :
basic-formal-sum: basic-formal-sum(K;S),
uall: ∀[x:A]. B[x],
member: t ∈ T,
bfs-predicate: bfs-predicate(K;S;p.P[p];b),
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_apply: x[s]
Lemmas referenced :
rng_car_wf,
bag-member_wf,
bag_wf,
istype-universe,
rng_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
introduction,
cut,
functionEquality,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
functionIsType,
productIsType,
universeEquality,
instantiate
Latex:
\mforall{}[K:RngSig]. \mforall{}[S:Type]. \mforall{}[P:(|K| \mtimes{} S) {}\mrightarrow{} \mBbbP{}]. \mforall{}[b:basic-formal-sum(K;S)].
(bfs-predicate(K;S;p.P[p];b) \mmember{} \mBbbP{})
Date html generated:
2019_10_31-AM-06_28_23
Last ObjectModification:
2019_08_19-AM-10_44_37
Theory : linear!algebra
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