Nuprl Lemma : rinv_functionality2
∀[x,y:ℝ]. (x ≠ r0 ⇒ (x = y) ⇒ (rinv(x) = rinv(y)))
Proof
Definitions occuring in Statement :
rneq: x ≠ y,
rinv: rinv(x),
req: x = y,
int-to-real: r(n),
real: ℝ,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
prop: ℙ,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
req_wf,
rneq_wf,
int-to-real_wf,
req_witness,
rinv_wf2,
real_wf,
req_weakening,
req_functionality,
rinv_functionality,
req_inversion,
rneq_functionality,
rnonzero_functionality,
rnonzero-iff
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
natural_numberEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
independent_functionElimination,
isect_memberEquality,
because_Cache,
independent_isectElimination,
productElimination
Latex:
\mforall{}[x,y:\mBbbR{}]. (x \mneq{} r0 {}\mRightarrow{} (x = y) {}\mRightarrow{} (rinv(x) = rinv(y)))
Date html generated:
2016_05_18-AM-07_11_01
Last ObjectModification:
2015_12_28-AM-00_39_35
Theory : reals
Home
Index