Nuprl Lemma : rleq_functionality
∀[x1,x2,y1,y2:ℝ]. (uiff(x1 ≤ y1;x2 ≤ y2)) supposing ((y1 = y2) and (x1 = x2))
Proof
Definitions occuring in Statement :
rleq: x ≤ y,
req: x = y,
real: ℝ,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
rleq: x ≤ y,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
rnonneg: rnonneg(x),
all: ∀x:A. B[x],
le: A ≤ B,
not: ¬A,
implies: P ⇒ Q,
false: False,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
real: ℝ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
less_than'_wf,
rsub_wf,
nat_plus_wf,
rnonneg_wf,
uiff_wf,
real_wf,
rleq_wf,
req_wf,
rnonneg_functionality,
rsub_functionality,
req_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
independent_pairFormation,
isect_memberFormation,
introduction,
cut,
hypothesis,
sqequalRule,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
productElimination,
independent_pairEquality,
voidElimination,
lemma_by_obid,
isectElimination,
applyEquality,
because_Cache,
minusEquality,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
setElimination,
rename,
isect_memberEquality,
addLevel,
independent_isectElimination,
independent_functionElimination
Latex:
\mforall{}[x1,x2,y1,y2:\mBbbR{}]. (uiff(x1 \mleq{} y1;x2 \mleq{} y2)) supposing ((y1 = y2) and (x1 = x2))
Date html generated:
2016_05_18-AM-07_05_16
Last ObjectModification:
2015_12_28-AM-00_36_27
Theory : reals
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