Nuprl Lemma : stable__rleq
∀[x,y:ℝ]. Stable{x ≤ y}
Proof
Definitions occuring in Statement :
rleq: x ≤ y,
real: ℝ,
stable: Stable{P},
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
stable: Stable{P},
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x],
real: ℝ,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
prop: ℙ,
false: False,
rleq: x ≤ y,
rnonneg: rnonneg(x),
le: A ≤ B,
subtype_rel: A ⊆r B
Lemmas referenced :
rleq-iff4,
decidable__le,
rleq_wf,
nat_plus_wf,
not_wf,
less_than'_wf,
rsub_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_functionElimination,
lambdaFormation,
dependent_functionElimination,
applyEquality,
setElimination,
rename,
addEquality,
natural_numberEquality,
unionElimination,
voidElimination,
sqequalRule,
lambdaEquality,
independent_pairEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
minusEquality
Latex:
\mforall{}[x,y:\mBbbR{}]. Stable\{x \mleq{} y\}
Date html generated:
2016_10_26-AM-09_06_33
Last ObjectModification:
2016_09_26-PM-00_35_12
Theory : reals
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