Nuprl Lemma : vs-tree-val_wf
∀[K:RngSig]. ∀[vs:VectorSpace(K)]. ∀[t:l_tree(Point(vs) × Top;|K|)]. (vs-tree-val(vs;t) ∈ Point(vs))
Proof
Definitions occuring in Statement :
vs-tree-val: vs-tree-val(vs;t),
vector-space: VectorSpace(K),
vs-point: Point(vs),
l_tree: l_tree(L;T),
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
product: x:A × B[x],
rng_car: |r|,
rng_sig: RngSig
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
vs-tree-val: vs-tree-val(vs;t),
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: so_lambda(x,y,z,w,v.t[x; y; z; w; v]),
so_apply: x[s1;s2;s3;s4;s5],
all: ∀x:A. B[x]
Lemmas referenced :
l_tree_ind_wf_simple,
vs-point_wf,
top_wf,
rng_car_wf,
pi1_wf_top,
vs-mul_wf,
vs-add_wf,
l_tree_wf,
vector-space_wf,
rng_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
productEquality,
hypothesisEquality,
hypothesis,
lambdaEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
dependent_functionElimination
Latex:
\mforall{}[K:RngSig]. \mforall{}[vs:VectorSpace(K)]. \mforall{}[t:l\_tree(Point(vs) \mtimes{} Top;|K|)].
(vs-tree-val(vs;t) \mmember{} Point(vs))
Date html generated:
2018_05_22-PM-09_42_05
Last ObjectModification:
2018_05_20-PM-10_41_53
Theory : linear!algebra
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