Nuprl Lemma : rv-between_functionality
∀n:ℕ. ∀a1,a2,b1,b2,c1,c2:ℝ^n. (req-vec(n;a1;a2) ⇒ req-vec(n;b1;b2) ⇒ req-vec(n;c1;c2) ⇒ (a1-b1-c1 ⇐⇒ a2-b2-c2))
Proof
Definitions occuring in Statement :
rv-between: a-b-c,
req-vec: req-vec(n;x;y),
real-vec: ℝ^n,
nat: ℕ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rv-between: a-b-c,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
rev_implies: P ⇐ Q,
uimplies: b supposing a
Lemmas referenced :
real-vec-between_functionality,
real-vec-sep_functionality,
real-vec-between_wf,
real-vec-sep_wf,
rv-between_wf,
req-vec_wf,
real-vec_wf,
nat_wf,
req-vec_inversion
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
sqequalHypSubstitution,
cut,
hypothesis,
addLevel,
productElimination,
thin,
introduction,
extract_by_obid,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
because_Cache,
levelHypothesis,
promote_hyp,
andLevelFunctionality,
isectElimination,
independent_isectElimination
Latex:
\mforall{}n:\mBbbN{}. \mforall{}a1,a2,b1,b2,c1,c2:\mBbbR{}\^{}n.
(req-vec(n;a1;a2) {}\mRightarrow{} req-vec(n;b1;b2) {}\mRightarrow{} req-vec(n;c1;c2) {}\mRightarrow{} (a1-b1-c1 \mLeftarrow{}{}\mRightarrow{} a2-b2-c2))
Date html generated:
2016_10_26-AM-10_31_52
Last ObjectModification:
2016_09_25-PM-00_55_29
Theory : reals
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