Nuprl Lemma : rneq-cotrans
∀x,y,z:ℝ. (x ≠ y ⇒ (x ≠ z ∨ y ≠ z))
Proof
Definitions occuring in Statement :
rneq: x ≠ y,
real: ℝ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
real_wf,
rneq_wf,
rneq-cases
Rules used in proof :
isectElimination,
independent_functionElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
hypothesis,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
extract_by_obid,
introduction,
cut
Latex:
\mforall{}x,y,z:\mBbbR{}. (x \mneq{} y {}\mRightarrow{} (x \mneq{} z \mvee{} y \mneq{} z))
Date html generated:
2018_07_29-AM-09_39_54
Last ObjectModification:
2018_06_28-PM-05_10_56
Theory : reals
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