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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