Nuprl Lemma : rsqrt-of-square
∀[x:{x:ℝ| r0 ≤ x} ]. (rsqrt(x * 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,
prop: ℙ,
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
rsqrt-unique,
square-nonneg,
rmul_wf,
rleq_wf,
int-to-real_wf,
rmul_comm,
req_inversion,
rsqrt_wf,
req_witness,
set_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesis,
dependent_set_memberEquality,
setElimination,
rename,
hypothesisEquality,
natural_numberEquality,
independent_isectElimination,
applyEquality,
sqequalRule,
independent_functionElimination,
lambdaEquality
Latex:
\mforall{}[x:\{x:\mBbbR{}| r0 \mleq{} x\} ]. (rsqrt(x * x) = x)
Date html generated:
2016_10_26-AM-10_09_21
Last ObjectModification:
2016_09_06-PM-07_00_25
Theory : reals
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