Nuprl Lemma : formal-sum_wf
∀[K:RngSig]. ∀[S:Type]. (formal-sum(K;S) ∈ Type)
Proof
Definitions occuring in Statement :
formal-sum: formal-sum(K;S),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type,
rng_sig: RngSig
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
formal-sum: formal-sum(K;S),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_sig_wf,
bfs-equiv-rel,
bfs-equiv_wf,
basic-formal-sum_wf,
quotient_wf
Rules used in proof :
isect_memberEquality,
universeEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
dependent_functionElimination,
independent_isectElimination,
because_Cache,
lambdaEquality,
hypothesis,
cumulativity,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[K:RngSig]. \mforall{}[S:Type]. (formal-sum(K;S) \mmember{} Type)
Date html generated:
2018_05_22-PM-09_45_16
Last ObjectModification:
2018_01_09-AM-11_07_40
Theory : linear!algebra
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