Nuprl Lemma : null-formal-sum-append
∀[K:RngSig]. ∀[S:Type]. ∀[fs1,fs2:basic-formal-sum(K;S)].
(null-formal-sum(K;S;fs1) ⇒ null-formal-sum(K;S;fs2) ⇒ null-formal-sum(K;S;fs1 + fs2))
Proof
Definitions occuring in Statement :
null-formal-sum: null-formal-sum(K;S;fs),
basic-formal-sum: basic-formal-sum(K;S),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
universe: Type,
rng_sig: RngSig,
bag-append: as + bs
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
basic-formal-sum: basic-formal-sum(K;S),
subtype_rel: A ⊆r B,
prop: ℙ,
member: t ∈ T,
exists: ∃x:A. B[x],
null-formal-sum: null-formal-sum(K;S;fs),
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
guard: {T},
uimplies: b supposing a,
squash: ↓T,
top: Top,
true: True
Lemmas referenced :
rng_sig_wf,
basic-formal-sum_wf,
null-formal-sum_wf,
exists_wf,
zero-bfs_wf,
neg-bfs_wf,
bag_wf,
equal_wf,
rng_car_wf,
bag-append_wf,
iff_weakening_equal,
bag-append-ac,
bag-append-assoc2,
squash_wf,
true_wf,
neg-bfs-append,
zero-bfs-append
Rules used in proof :
universeEquality,
lambdaEquality,
sqequalRule,
applyEquality,
equalitySymmetry,
equalityTransitivity,
because_Cache,
cumulativity,
hypothesis,
hypothesisEquality,
productEquality,
isectElimination,
extract_by_obid,
introduction,
cut,
dependent_pairFormation,
thin,
productElimination,
sqequalHypSubstitution,
lambdaFormation,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
independent_functionElimination,
independent_isectElimination,
baseClosed,
imageMemberEquality,
imageElimination,
voidEquality,
voidElimination,
isect_memberEquality,
natural_numberEquality,
levelHypothesis,
equalityUniverse
Latex:
\mforall{}[K:RngSig]. \mforall{}[S:Type]. \mforall{}[fs1,fs2:basic-formal-sum(K;S)].
(null-formal-sum(K;S;fs1) {}\mRightarrow{} null-formal-sum(K;S;fs2) {}\mRightarrow{} null-formal-sum(K;S;fs1 + fs2))
Date html generated:
2018_05_22-PM-09_47_13
Last ObjectModification:
2018_01_09-PM-06_08_50
Theory : linear!algebra
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