Nuprl Lemma : log-contraction_wf
∀[a,x:ℝ]. log-contraction(a;x) ∈ ℝ supposing r0 < a
Proof
Definitions occuring in Statement :
log-contraction: log-contraction(a;x),
rless: x < y,
int-to-real: r(n),
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
log-contraction: log-contraction(a;x),
prop: ℙ,
all: ∀x:A. B[x],
rneq: x ≠ y,
or: P ∨ Q,
rev_implies: P ⇐ Q,
rge: x ≥ y,
rgt: x > y,
implies: P ⇒ Q,
guard: {T},
and: P ∧ Q,
iff: P ⇐⇒ Q
Lemmas referenced :
radd_wf,
rmul_wf,
int-to-real_wf,
rdiv_wf,
rsub_wf,
rexp_wf,
rless_wf,
real_wf,
rexp-positive,
rless_functionality_wrt_implies,
rleq_weakening_equal,
rleq_weakening_rless,
radd_functionality_wrt_rless1,
rless_functionality,
req_weakening,
radd-zero-both,
radd_comm
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
natural_numberEquality,
hypothesis,
because_Cache,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
dependent_functionElimination,
inrFormation,
independent_functionElimination,
addLevel,
productElimination
Latex:
\mforall{}[a,x:\mBbbR{}]. log-contraction(a;x) \mmember{} \mBbbR{} supposing r0 < a
Date html generated:
2016_10_26-PM-00_29_07
Last ObjectModification:
2016_09_12-PM-05_44_45
Theory : reals_2
Home
Index