Nuprl Lemma : real-vec-subtype
∀[n,m:ℕ]. ℝ^m ⊆r ℝ^n supposing n ≤ m
Proof
Definitions occuring in Statement :
real-vec: ℝ^n,
nat: ℕ,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
le: A ≤ B
Definitions unfolded in proof :
real-vec: ℝ^n,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
and: P ∧ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B
Lemmas referenced :
subtype_rel_dep_function,
int_seg_wf,
real_wf,
int_seg_subtype,
false_wf,
subtype_rel_self,
le_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
lambdaEquality,
because_Cache,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[n,m:\mBbbN{}]. \mBbbR{}\^{}m \msubseteq{}r \mBbbR{}\^{}n supposing n \mleq{} m
Date html generated:
2017_10_03-AM-10_47_09
Last ObjectModification:
2017_06_15-PM-01_01_30
Theory : reals
Home
Index