Nuprl Lemma : vs-map-eq
∀[K:RngSig]. ∀[A,B:VectorSpace(K)]. ∀[f:A ⟶ B]. ∀[g:Point(A) ⟶ Point(B)].
f = g ∈ A ⟶ B supposing f = g ∈ (Point(A) ⟶ Point(B))
Proof
Definitions occuring in Statement :
vs-map: A ⟶ B,
vector-space: VectorSpace(K),
vs-point: Point(vs),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
equal: s = t ∈ T,
rng_sig: RngSig
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
vs-map: A ⟶ B,
and: P ∧ Q,
all: ∀x:A. B[x],
member: t ∈ T
Lemmas referenced :
vs-point_wf,
vs-add_wf,
rng_car_wf,
vs-mul_wf,
vs-map_wf,
vector-space_wf,
rng_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
sqequalHypSubstitution,
setElimination,
thin,
rename,
cut,
dependent_set_memberEquality_alt,
hypothesis,
sqequalRule,
productIsType,
functionIsType,
universeIsType,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
because_Cache,
equalityIstype,
applyEquality,
dependent_functionElimination
Latex:
\mforall{}[K:RngSig]. \mforall{}[A,B:VectorSpace(K)]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[g:Point(A) {}\mrightarrow{} Point(B)]. f = g supposing f = g
Date html generated:
2019_10_31-AM-06_26_52
Last ObjectModification:
2019_08_01-AM-10_35_41
Theory : linear!algebra
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