Nuprl Lemma : bfs-rm0_wf
∀[K:RngSig]. ∀[S:Type]. ∀[b:basic-formal-sum(K;S)]. ∀[eq:EqDecider(|K|)]. (bfs-rm0(K;eq;b) ∈ basic-formal-sum(K;S))
Proof
Definitions occuring in Statement :
bfs-rm0: bfs-rm0(K;eq;b),
basic-formal-sum: basic-formal-sum(K;S),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
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-rm0: bfs-rm0(K;eq;b),
so_lambda: λ2x.t[x],
deq: EqDecider(T),
top: Top,
so_apply: x[s],
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a
Lemmas referenced :
bag-filter_wf,
rng_car_wf,
bnot_wf,
pi1_wf_top,
istype-void,
rng_zero_wf,
subtype_rel_bag,
assert_wf,
istype-assert,
deq_wf,
bag_wf,
istype-universe,
rng_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
productEquality,
hypothesisEquality,
hypothesis,
lambdaEquality_alt,
applyEquality,
setElimination,
rename,
productElimination,
independent_pairEquality,
isect_memberEquality_alt,
voidElimination,
productIsType,
universeIsType,
setEquality,
independent_isectElimination,
setIsType,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isectIsTypeImplies,
inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}[K:RngSig]. \mforall{}[S:Type]. \mforall{}[b:basic-formal-sum(K;S)]. \mforall{}[eq:EqDecider(|K|)].
(bfs-rm0(K;eq;b) \mmember{} basic-formal-sum(K;S))
Date html generated:
2019_10_31-AM-06_28_41
Last ObjectModification:
2019_08_27-PM-03_10_12
Theory : linear!algebra
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