Nuprl Lemma : vector-mul_wf
∀[i:Type]. ∀[r:RngSig]. ∀[c:|r|]. ∀[a:i ⟶ |r|]. ((c*a) ∈ i ⟶ |r|)
Proof
Definitions occuring in Statement :
vector-mul: (c*a),
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type,
rng_car: |r|,
rng_sig: RngSig
Definitions unfolded in proof :
infix_ap: x f y,
vector-mul: (c*a),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_sig_wf,
rng_car_wf,
rng_times_wf
Rules used in proof :
universeEquality,
because_Cache,
isect_memberEquality,
functionEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
cumulativity,
functionExtensionality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
applyEquality,
lambdaEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[i:Type]. \mforall{}[r:RngSig]. \mforall{}[c:|r|]. \mforall{}[a:i {}\mrightarrow{} |r|]. ((c*a) \mmember{} i {}\mrightarrow{} |r|)
Date html generated:
2018_05_21-PM-09_40_35
Last ObjectModification:
2017_12_18-PM-00_17_09
Theory : matrices
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