Nuprl Lemma : rinv-rminus
∀[x:ℝ]. -(rinv(x)) = rinv(-(x)) supposing x ≠ r0
Proof
Definitions occuring in Statement :
rneq: x ≠ y,
rinv: rinv(x),
req: x = y,
rminus: -(x),
int-to-real: r(n),
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
itermConstant: "const",
req_int_terms: t1 ≡ t2,
false: False,
not: ¬A,
top: Top
Lemmas referenced :
rmul-inverse-is-rinv,
rminus_wf,
rminus-neq-zero,
rinv_wf2,
rneq_wf,
int-to-real_wf,
real_wf,
rmul_wf,
req_functionality,
rmul_functionality,
rminus-as-rmul,
req_weakening,
req_transitivity,
real_term_polynomial,
itermSubtract_wf,
itermMultiply_wf,
itermConstant_wf,
itermVar_wf,
real_term_value_const_lemma,
real_term_value_sub_lemma,
real_term_value_mul_lemma,
real_term_value_var_lemma,
req-iff-rsub-is-0,
rmul-identity1,
rmul-rinv
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
natural_numberEquality,
minusEquality,
because_Cache,
productElimination,
sqequalRule,
computeAll,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[x:\mBbbR{}]. -(rinv(x)) = rinv(-(x)) supposing x \mneq{} r0
Date html generated:
2017_10_03-AM-08_27_58
Last ObjectModification:
2017_07_28-AM-07_24_56
Theory : reals
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