Nuprl Lemma : formal-sum-add_wf1
∀[S:Type]. ∀[K:RngSig]. ∀[x,y:basic-formal-sum(K;S)]. (x + y ∈ basic-formal-sum(K;S))
Proof
Definitions occuring in Statement :
formal-sum-add: x + y,
basic-formal-sum: basic-formal-sum(K;S),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type,
rng_sig: RngSig
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
basic-formal-sum: basic-formal-sum(K;S),
formal-sum-add: x + y
Lemmas referenced :
rng_sig_wf,
bag_wf,
rng_car_wf,
bag-append_wf
Rules used in proof :
universeEquality,
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
cumulativity,
hypothesis,
hypothesisEquality,
productEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}[S:Type]. \mforall{}[K:RngSig]. \mforall{}[x,y:basic-formal-sum(K;S)]. (x + y \mmember{} basic-formal-sum(K;S))
Date html generated:
2018_05_22-PM-09_45_20
Last ObjectModification:
2018_01_09-PM-00_10_55
Theory : linear!algebra
Home
Index