Nuprl Lemma : bfs-reduce_wf
∀[K:RngSig]. ∀[S:Type]. ∀[as,bs:basic-formal-sum(K;S)]. (bfs-reduce(K;S;as;bs) ∈ ℙ)
Proof
Definitions occuring in Statement :
bfs-reduce: bfs-reduce(K;S;as;bs),
basic-formal-sum: basic-formal-sum(K;S),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type,
rng_sig: RngSig
Definitions unfolded in proof :
infix_ap: x f y,
and: P ∧ Q,
prop: ℙ,
so_apply: x[s],
subtype_rel: A ⊆r B,
basic-formal-sum: basic-formal-sum(K;S),
so_lambda: λ2x.t[x],
bfs-reduce: bfs-reduce(K;S;as;bs),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_sig_wf,
rng_plus_wf,
infix_ap_wf,
formal-sum-mul_wf1,
zero-bfs_wf,
rng_car_wf,
bag-append_wf,
basic-formal-sum_wf,
equal_wf,
bag_wf,
exists_wf,
or_wf
Rules used in proof :
universeEquality,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
applyEquality,
productEquality,
because_Cache,
lambdaEquality,
hypothesis,
hypothesisEquality,
cumulativity,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[K:RngSig]. \mforall{}[S:Type]. \mforall{}[as,bs:basic-formal-sum(K;S)]. (bfs-reduce(K;S;as;bs) \mmember{} \mBbbP{})
Date html generated:
2018_05_22-PM-09_44_40
Last ObjectModification:
2018_05_18-PM-04_42_36
Theory : linear!algebra
Home
Index