Nuprl Lemma : rexp-of-positive
∀x:ℝ. ((r0 < x) ⇒ (r1 < e^x))
Proof
Definitions occuring in Statement :
rexp: e^x,
rless: x < y,
int-to-real: r(n),
real: ℝ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
guard: {T},
uimplies: b supposing a,
and: P ∧ Q,
uiff: uiff(P;Q),
rev_implies: P ⇐ Q,
rge: x ≥ y
Lemmas referenced :
rless_wf,
int-to-real_wf,
real_wf,
radd_wf,
rexp_wf,
rleq_weakening_rless,
trivial-rless-radd,
rless_functionality_wrt_implies,
rleq_weakening_equal,
rexp-of-nonneg-stronger
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
hypothesisEquality,
because_Cache,
independent_isectElimination,
dependent_functionElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}x:\mBbbR{}. ((r0 < x) {}\mRightarrow{} (r1 < e\^{}x))
Date html generated:
2016_10_26-AM-09_28_08
Last ObjectModification:
2016_09_19-PM-11_00_07
Theory : reals
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