Nuprl Lemma : rfun_subtype
∀[I,J:Interval]. I ⟶ℝ ⊆r J ⟶ℝ supposing J ⊆ I
Proof
Definitions occuring in Statement :
subinterval: I ⊆ J ,
rfun: I ⟶ℝ,
interval: Interval,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
rfun: I ⟶ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
subinterval: I ⊆ J
Lemmas referenced :
subtype_rel_dep_function,
real_wf,
i-member_wf,
subtype_rel_sets,
subtype_rel_self,
set_wf,
subinterval_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setEquality,
hypothesis,
hypothesisEquality,
lambdaEquality,
independent_isectElimination,
because_Cache,
setElimination,
rename,
lambdaFormation,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[I,J:Interval]. I {}\mrightarrow{}\mBbbR{} \msubseteq{}r J {}\mrightarrow{}\mBbbR{} supposing J \msubseteq{} I
Date html generated:
2016_05_18-AM-08_51_29
Last ObjectModification:
2015_12_27-PM-11_42_51
Theory : reals
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