Nuprl Lemma : rsqrt_functionality
∀[x:{x:ℝ| r0 ≤ x} ]. ∀[y:ℝ]. rsqrt(x) = rsqrt(y) supposing x = y
Proof
Definitions occuring in Statement :
rsqrt: rsqrt(x),
rleq: x ≤ y,
req: x = y,
int-to-real: r(n),
real: ℝ,
uimplies: b supposing a,
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,
uimplies: b supposing a,
rsqrt: rsqrt(x),
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ,
guard: {T},
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
int_upper: {i...},
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
all: ∀x:A. B[x],
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
req_witness,
rsqrt_wf,
real_wf,
and_wf,
rleq_wf,
int-to-real_wf,
req_wf,
rmul_wf,
rleq_transitivity,
rleq_weakening,
set_wf,
rroot_wf,
false_wf,
le_wf,
subtype_rel_sets,
assert_wf,
isEven_wf,
req_weakening,
req_functionality,
rroot_functionality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
natural_numberEquality,
sqequalRule,
dependent_set_memberEquality,
independent_isectElimination,
because_Cache,
independent_functionElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
independent_pairFormation,
lambdaFormation,
functionEquality,
productElimination
Latex:
\mforall{}[x:\{x:\mBbbR{}| r0 \mleq{} x\} ]. \mforall{}[y:\mBbbR{}]. rsqrt(x) = rsqrt(y) supposing x = y
Date html generated:
2016_05_18-AM-09_43_07
Last ObjectModification:
2015_12_27-PM-11_16_07
Theory : reals
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