Nuprl Lemma : rv-between-inner-trans
∀n:ℕ. ∀a,b,c,d:ℝ^n. (a-b-d ⇒ b-c-d ⇒ a-b-c)
Proof
Definitions occuring in Statement :
rv-between: a-b-c,
real-vec: ℝ^n,
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
prop: ℙ,
rv-between: a-b-c,
and: P ∧ Q,
cand: A c∧ B,
real-vec-sep: a ≠ b,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
rge: x ≥ y,
rgt: x > y,
guard: {T}
Lemmas referenced :
real-vec-between-inner-trans,
real-vec_wf,
nat_wf,
rv-between_wf,
rv-between-sep,
real-vec-dist-between,
int-to-real_wf,
real-vec-dist_wf,
real_wf,
rleq_wf,
radd_wf,
rless_functionality,
req_weakening,
trivial-rless-radd,
rless_functionality_wrt_implies,
rleq_weakening_equal,
rleq_weakening_rless,
radd_functionality_wrt_rless1
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
independent_functionElimination,
because_Cache,
productElimination,
independent_pairFormation,
natural_numberEquality,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
sqequalRule,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}n:\mBbbN{}. \mforall{}a,b,c,d:\mBbbR{}\^{}n. (a-b-d {}\mRightarrow{} b-c-d {}\mRightarrow{} a-b-c)
Date html generated:
2016_10_26-AM-10_38_23
Last ObjectModification:
2016_09_25-AM-00_17_58
Theory : reals
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