Nuprl Lemma : trivial-vs_wf
∀[K:RngSig]. (0 ∈ VectorSpace(K))
Proof
Definitions occuring in Statement :
trivial-vs: 0,
vector-space: VectorSpace(K),
uall: ∀[x:A]. B[x],
member: t ∈ T,
rng_sig: RngSig
Definitions unfolded in proof :
all: ∀x:A. B[x],
cand: A c∧ B,
and: P ∧ Q,
uimplies: b supposing a,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
trivial-vs: 0,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_sig_wf,
equal-unit,
rng_car_wf,
it_wf,
unit_wf2,
mk-vs_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
independent_pairFormation,
lambdaFormation,
independent_isectElimination,
because_Cache,
lambdaEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[K:RngSig]. (0 \mmember{} VectorSpace(K))
Date html generated:
2018_05_22-PM-09_41_50
Last ObjectModification:
2018_01_09-AM-10_40_56
Theory : linear!algebra
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