Nuprl Lemma : lgc_wf
∀[a,x:ℝ]. lgc(a;x) ∈ ℝ supposing r0 < a
Proof
Definitions occuring in Statement :
lgc: lgc(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,
lgc: lgc(a;x),
subtype_rel: A ⊆r B,
prop: ℙ,
all: ∀x:A. B[x],
rneq: x ≠ y,
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
uiff: uiff(P;Q),
rge: x ≥ y,
rgt: x > y,
guard: {T}
Lemmas referenced :
radd_wf,
rsub_wf,
int-to-real_wf,
int-rmul_wf,
rdiv_wf,
real_exp_wf,
rless_wf,
real_wf,
rexp-positive,
rexp_wf,
rless_functionality,
req_weakening,
radd_functionality,
real_exp-req,
trivial-rless-radd,
rless_functionality_wrt_implies,
rleq_weakening_equal,
rleq_weakening_rless,
radd_functionality_wrt_rless1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
closedConclusion,
natural_numberEquality,
hypothesis,
because_Cache,
applyEquality,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
dependent_functionElimination,
inrFormation_alt,
lambdaEquality_alt,
setElimination,
rename,
productElimination,
independent_functionElimination
Latex:
\mforall{}[a,x:\mBbbR{}]. lgc(a;x) \mmember{} \mBbbR{} supposing r0 < a
Date html generated:
2019_10_31-AM-06_08_40
Last ObjectModification:
2019_04_03-AM-01_15_30
Theory : reals_2
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