Nuprl Lemma : rv-between_functionality3
∀n:ℕ. ∀a1,a2,b1,b2,c1,c2:ℝ^n. ((¬a1 ≠ a2) ⇒ (¬b1 ≠ b2) ⇒ (¬c1 ≠ c2) ⇒ a1-b1-c1 ⇒ a2-b2-c2)
Proof
Definitions occuring in Statement :
rv-between: a-b-c,
real-vec-sep: a ≠ b,
real-vec: ℝ^n,
nat: ℕ,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
prop: ℙ,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rv-between_functionality2,
not_wf,
real-vec-sep_wf,
real-vec_wf,
nat_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_functionElimination,
productElimination,
isectElimination
Latex:
\mforall{}n:\mBbbN{}. \mforall{}a1,a2,b1,b2,c1,c2:\mBbbR{}\^{}n. ((\mneg{}a1 \mneq{} a2) {}\mRightarrow{} (\mneg{}b1 \mneq{} b2) {}\mRightarrow{} (\mneg{}c1 \mneq{} c2) {}\mRightarrow{} a1-b1-c1 {}\mRightarrow{} a2-b2-c2)
Date html generated:
2016_10_26-AM-10_32_18
Last ObjectModification:
2016_09_26-PM-09_27_00
Theory : reals
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