Nuprl Lemma : lgc-req
∀[a,x:ℝ]. lgc(a;x) = log-contraction(a;x) supposing r0 < a
Proof
Definitions occuring in Statement :
lgc: lgc(a;x),
log-contraction: log-contraction(a;x),
rless: x < y,
req: x = y,
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],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
log-contraction: log-contraction(a;x),
lgc: lgc(a;x),
implies: P ⇒ Q,
prop: ℙ,
and: P ∧ Q,
uiff: uiff(P;Q),
rev_implies: P ⇐ Q,
rge: x ≥ y,
rgt: x > y,
guard: {T},
sq_stable: SqStable(P),
squash: ↓T,
rneq: x ≠ y,
or: P ∨ Q,
iff: P ⇐⇒ Q,
rev_uimplies: rev_uimplies(P;Q),
rdiv: (x/y),
req_int_terms: t1 ≡ t2,
false: False,
not: ¬A,
top: Top
Lemmas referenced :
rexp-positive,
req_witness,
lgc_wf,
log-contraction_wf,
rless_wf,
int-to-real_wf,
real_wf,
radd_wf,
rexp_wf,
trivial-rless-radd,
rless_functionality_wrt_implies,
rleq_weakening_equal,
rleq_weakening_rless,
radd_functionality_wrt_rless1,
real_exp_wf,
sq_stable__req,
rsub_wf,
int-rmul_wf,
rdiv_wf,
rmul_wf,
rless_functionality,
req_weakening,
radd_functionality,
req_functionality,
int-rmul_functionality,
rdiv_functionality,
rmul_preserves_req,
rinv_wf2,
itermSubtract_wf,
itermMultiply_wf,
itermAdd_wf,
itermVar_wf,
itermConstant_wf,
int-rmul-req,
req_transitivity,
rmul_functionality,
rmul-rinv3,
req-iff-rsub-is-0,
real_polynomial_null,
istype-int,
real_term_value_sub_lemma,
istype-void,
real_term_value_mul_lemma,
real_term_value_add_lemma,
real_term_value_var_lemma,
real_term_value_const_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
independent_isectElimination,
hypothesis,
independent_functionElimination,
universeIsType,
natural_numberEquality,
sqequalRule,
isect_memberEquality_alt,
because_Cache,
isectIsTypeImplies,
inhabitedIsType,
productElimination,
equalityTransitivity,
equalitySymmetry,
lambdaFormation_alt,
setElimination,
rename,
equalityIstype,
imageMemberEquality,
baseClosed,
imageElimination,
closedConclusion,
inrFormation_alt,
minusEquality,
approximateComputation,
lambdaEquality_alt,
int_eqEquality,
voidElimination
Latex:
\mforall{}[a,x:\mBbbR{}]. lgc(a;x) = log-contraction(a;x) supposing r0 < a
Date html generated:
2019_10_31-AM-06_08_47
Last ObjectModification:
2019_02_04-PM-10_56_15
Theory : reals_2
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