Nuprl Lemma : stable__real-fun
∀[a,b:ℝ]. ∀[f:[a, b] ⟶ℝ]. Stable{real-fun(f;a;b)}
Proof
Definitions occuring in Statement :
real-fun: real-fun(f;a;b),
rfun: I ⟶ℝ,
rccint: [l, u],
real: ℝ,
stable: Stable{P},
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
real-fun: real-fun(f;a;b),
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
rfun: I ⟶ℝ,
so_apply: x[s],
stable: Stable{P},
uimplies: b supposing a
Lemmas referenced :
stable__all,
real_wf,
i-member_wf,
rccint_wf,
all_wf,
req_wf,
stable_req,
set_wf,
req_witness,
not_wf,
rfun_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setEquality,
hypothesis,
hypothesisEquality,
lambdaEquality,
lambdaFormation,
setElimination,
rename,
dependent_functionElimination,
functionEquality,
applyEquality,
dependent_set_memberEquality,
because_Cache,
independent_functionElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[a,b:\mBbbR{}]. \mforall{}[f:[a, b] {}\mrightarrow{}\mBbbR{}]. Stable\{real-fun(f;a;b)\}
Date html generated:
2017_10_03-AM-09_56_44
Last ObjectModification:
2017_09_26-AM-02_20_16
Theory : reals
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