Nuprl Lemma : rfun-eq_wf
∀[I:Interval]. ∀[f,g:I ⟶ℝ]. (rfun-eq(I;f;g) ∈ ℙ)
Proof
Definitions occuring in Statement :
rfun-eq: rfun-eq(I;f;g),
rfun: I ⟶ℝ,
interval: Interval,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rfun-eq: rfun-eq(I;f;g),
prop: ℙ,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
so_apply: x[s]
Lemmas referenced :
all_wf,
real_wf,
i-member_wf,
req_wf,
r-ap_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,
independent_isectElimination,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[I:Interval]. \mforall{}[f,g:I {}\mrightarrow{}\mBbbR{}]. (rfun-eq(I;f;g) \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-08_42_10
Last ObjectModification:
2015_12_27-PM-11_51_03
Theory : reals
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