Nuprl Lemma : rneq_functionality
∀x1,x2,y1,y2:ℝ. (x1 ≠ y1 ⇐⇒ x2 ≠ y2) supposing ((y1 = y2) and (x1 = x2))
Proof
Definitions occuring in Statement :
rneq: x ≠ y,
req: x = y,
real: ℝ,
uimplies: b supposing a,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
rneq: x ≠ y,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
or: P ∨ Q
Lemmas referenced :
req_witness,
req_wf,
real_wf,
or_wf,
rless_wf,
iff_wf,
rless_functionality,
req_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
introduction,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
rename,
independent_pairFormation,
because_Cache,
addLevel,
productElimination,
impliesFunctionality,
orFunctionality,
dependent_functionElimination,
independent_isectElimination,
orLevelFunctionality
Latex:
\mforall{}x1,x2,y1,y2:\mBbbR{}. (x1 \mneq{} y1 \mLeftarrow{}{}\mRightarrow{} x2 \mneq{} y2) supposing ((y1 = y2) and (x1 = x2))
Date html generated:
2016_05_18-AM-07_10_32
Last ObjectModification:
2015_12_28-AM-00_38_44
Theory : reals
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