Nuprl Lemma : rminus-reverses-rless
∀x,y:ℝ. ((x < y) ⇒ (-(y) < -(x)))
Proof
Definitions occuring in Statement :
rless: x < y,
rminus: -(x),
real: ℝ,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
itermConstant: "const",
req_int_terms: t1 ≡ t2,
false: False,
not: ¬A,
top: Top,
uiff: uiff(P;Q),
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
rless-implies-rless,
rminus_wf,
real_term_polynomial,
itermSubtract_wf,
itermVar_wf,
itermMinus_wf,
int-to-real_wf,
real_term_value_const_lemma,
real_term_value_sub_lemma,
real_term_value_var_lemma,
real_term_value_minus_lemma,
req-iff-rsub-is-0,
rsub_wf,
rless_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
hypothesisEquality,
hypothesis,
independent_isectElimination,
natural_numberEquality,
sqequalRule,
computeAll,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
productElimination
Latex:
\mforall{}x,y:\mBbbR{}. ((x < y) {}\mRightarrow{} (-(y) < -(x)))
Date html generated:
2017_10_03-AM-08_26_32
Last ObjectModification:
2017_07_28-AM-07_24_23
Theory : reals
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