Nuprl Lemma : rminus-reverses-rleq
∀[x,y:ℝ]. -(y) ≤ -(x) supposing x ≤ y
Proof
Definitions occuring in Statement :
rleq: x ≤ y,
rminus: -(x),
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
rleq: x ≤ y,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
rnonneg: rnonneg(x),
all: ∀x:A. B[x],
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
real: ℝ,
prop: ℙ,
rsub: x - y,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
less_than'_wf,
rsub_wf,
rminus_wf,
real_wf,
nat_plus_wf,
rnonneg_wf,
rnonneg_functionality,
radd_wf,
radd_comm,
radd_functionality,
rminus-rminus,
req_weakening
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
productElimination,
independent_pairEquality,
because_Cache,
lemma_by_obid,
isectElimination,
applyEquality,
hypothesis,
setElimination,
rename,
minusEquality,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
voidElimination,
independent_isectElimination,
independent_functionElimination,
promote_hyp,
addLevel
Latex:
\mforall{}[x,y:\mBbbR{}]. -(y) \mleq{} -(x) supposing x \mleq{} y
Date html generated:
2016_05_18-AM-07_07_24
Last ObjectModification:
2015_12_28-AM-00_38_51
Theory : reals
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