Nuprl Lemma : real-vec-between_wf
∀[n:ℕ]. ∀[a,b,c:ℝ^n]. (a-b-c ∈ ℙ)
Proof
Definitions occuring in Statement :
real-vec-between: a-b-c,
real-vec: ℝ^n,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
real-vec-between: a-b-c,
all: ∀x:A. B[x],
top: Top,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s]
Lemmas referenced :
member_rooint_lemma,
exists_wf,
real_wf,
rless_wf,
int-to-real_wf,
req-vec_wf,
real-vec-add_wf,
real-vec-mul_wf,
rsub_wf,
real-vec_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isectElimination,
lambdaEquality,
productEquality,
natural_numberEquality,
hypothesisEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[a,b,c:\mBbbR{}\^{}n]. (a-b-c \mmember{} \mBbbP{})
Date html generated:
2016_10_26-AM-10_17_32
Last ObjectModification:
2016_09_24-PM-09_28_25
Theory : reals
Home
Index