Nuprl Lemma : increasing-on-interval_wf
∀[I:Interval]. ∀[f:I ⟶ℝ]. (f[x] increasing for x ∈ I ∈ ℙ)
Proof
Definitions occuring in Statement :
increasing-on-interval: f[x] increasing for x ∈ I,
rfun: I ⟶ℝ,
interval: Interval,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
increasing-on-interval: f[x] increasing for x ∈ I,
prop: ℙ,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_apply: x[s],
rfun: I ⟶ℝ
Lemmas referenced :
all_wf,
real_wf,
i-member_wf,
rless_wf,
rleq_wf,
rfun_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setEquality,
hypothesis,
hypothesisEquality,
lambdaEquality,
lambdaFormation,
setElimination,
rename,
because_Cache,
functionEquality,
applyEquality,
dependent_set_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[I:Interval]. \mforall{}[f:I {}\mrightarrow{}\mBbbR{}]. (f[x] increasing for x \mmember{} I \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-10_17_53
Last ObjectModification:
2015_12_27-PM-10_57_11
Theory : reals
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