Nuprl Lemma : rsqrt_nonneg
∀[x:{x:ℝ| r0 ≤ x} ]. (r0 ≤ rsqrt(x))
Proof
Definitions occuring in Statement :
rsqrt: rsqrt(x),
rleq: x ≤ y,
int-to-real: r(n),
real: ℝ,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
and: P ∧ Q,
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
sq_stable: SqStable(P),
squash: ↓T,
rleq: x ≤ y,
rnonneg: rnonneg(x),
le: A ≤ B,
not: ¬A,
false: False,
subtype_rel: A ⊆r B,
real: ℝ
Lemmas referenced :
nat_plus_wf,
rsub_wf,
less_than'_wf,
equal_wf,
sq_stable__rleq,
rmul_wf,
req_wf,
int-to-real_wf,
rleq_wf,
and_wf,
real_wf,
set_wf,
rsqrt_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
natural_numberEquality,
setElimination,
rename,
lambdaFormation,
independent_functionElimination,
productElimination,
imageMemberEquality,
baseClosed,
imageElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_pairEquality,
voidElimination,
applyEquality,
setEquality,
minusEquality,
axiomEquality
Latex:
\mforall{}[x:\{x:\mBbbR{}| r0 \mleq{} x\} ]. (r0 \mleq{} rsqrt(x))
Date html generated:
2016_05_18-AM-09_43_19
Last ObjectModification:
2016_01_17-AM-02_49_04
Theory : reals
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