Nuprl Lemma : rsqrt_squared
∀[x:{x:ℝ| r0 ≤ x} ]. ((rsqrt(x) * rsqrt(x)) = x)
Proof
Definitions occuring in Statement :
rsqrt: rsqrt(x),
rleq: x ≤ y,
req: x = y,
rmul: a * b,
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,
subtype_rel: A ⊆r B
Lemmas referenced :
req_witness,
equal_wf,
sq_stable__req,
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,
applyEquality,
setEquality,
because_Cache
Latex:
\mforall{}[x:\{x:\mBbbR{}| r0 \mleq{} x\} ]. ((rsqrt(x) * rsqrt(x)) = x)
Date html generated:
2016_05_18-AM-09_43_29
Last ObjectModification:
2016_01_17-AM-02_49_31
Theory : reals
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