Nuprl Lemma : sq_stable__rleq
∀[x,y:ℝ]. SqStable(x ≤ y)
Proof
Definitions occuring in Statement :
rleq: x ≤ y,
real: ℝ,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
rleq: x ≤ y,
uall: ∀[x:A]. B[x],
member: t ∈ T,
sq_stable: SqStable(P),
implies: P ⇒ Q,
rnonneg: rnonneg(x),
all: ∀x:A. B[x],
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
false: False,
subtype_rel: A ⊆r B,
real: ℝ,
prop: ℙ
Lemmas referenced :
sq_stable__rnonneg,
rsub_wf,
less_than'_wf,
real_wf,
nat_plus_wf,
squash_wf,
rnonneg_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
dependent_functionElimination,
productElimination,
independent_pairEquality,
because_Cache,
applyEquality,
setElimination,
rename,
minusEquality,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
voidElimination
Latex:
\mforall{}[x,y:\mBbbR{}]. SqStable(x \mleq{} y)
Date html generated:
2016_05_18-AM-07_05_10
Last ObjectModification:
2015_12_28-AM-00_36_02
Theory : reals
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