Nuprl Lemma : rnexp2-nonneg
∀x:ℝ. (r0 ≤ x^2)
Proof
Definitions occuring in Statement :
rleq: x ≤ y,
rnexp: x^k1,
int-to-real: r(n),
real: ℝ,
all: ∀x:A. B[x],
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
squash: ↓T,
nat_plus: ℕ+,
less_than: a < b,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
rnexp-even-nonneg,
false_wf,
le_wf,
equal_wf,
squash_wf,
true_wf,
rem_eq_args,
less_than_wf,
iff_weakening_equal,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
hypothesis,
isectElimination,
hypothesisEquality,
independent_functionElimination,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
intEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
because_Cache
Latex:
\mforall{}x:\mBbbR{}. (r0 \mleq{} x\^{}2)
Date html generated:
2017_10_03-AM-08_32_51
Last ObjectModification:
2017_07_28-AM-07_27_58
Theory : reals
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