Nuprl Lemma : rsqrt-is-zero
∀[x:{x:ℝ| r0 ≤ x} ]. (rsqrt(x) = r0 ⇐⇒ x = r0)
Proof
Definitions occuring in Statement :
rsqrt: rsqrt(x),
rleq: x ≤ y,
req: x = y,
int-to-real: r(n),
real: ℝ,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
set: {x:A| B[x]} ,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
uimplies: b supposing a,
uiff: uiff(P;Q)
Lemmas referenced :
req_witness,
int-to-real_wf,
req_wf,
rsqrt_wf,
rleq_wf,
real_wf,
rmul_wf,
set_wf,
square-is-zero,
iff_wf,
req_functionality,
rsqrt_squared,
req_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
hypothesisEquality,
extract_by_obid,
isectElimination,
setElimination,
rename,
hypothesis,
natural_numberEquality,
independent_functionElimination,
dependent_set_memberEquality,
applyEquality,
setEquality,
productEquality,
addLevel,
independent_pairFormation,
impliesFunctionality,
because_Cache,
lambdaFormation,
independent_isectElimination
Latex:
\mforall{}[x:\{x:\mBbbR{}| r0 \mleq{} x\} ]. (rsqrt(x) = r0 \mLeftarrow{}{}\mRightarrow{} x = r0)
Date html generated:
2016_10_26-AM-10_08_06
Last ObjectModification:
2016_09_14-PM-05_36_44
Theory : reals
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