### Nuprl Lemma : subtype_rel-int_seg

`∀[m1,n1,m2,n2:ℤ].  {m1..n1-} ⊆r {m2..n2-} supposing (m2 ≤ m1) ∧ (n1 ≤ n2)`

Proof

Definitions occuring in Statement :  int_seg: `{i..j-}` uimplies: `b supposing a` subtype_rel: `A ⊆r B` uall: `∀[x:A]. B[x]` le: `A ≤ B` and: `P ∧ Q` int: `ℤ`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` and: `P ∧ Q` subtype_rel: `A ⊆r B` prop: `ℙ`
Lemmas referenced :  int_seg_subtype and_wf le_wf
Rules used in proof :  comment sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalHypSubstitution productElimination thin lemma_by_obid isectElimination hypothesisEquality independent_isectElimination independent_pairFormation hypothesis sqequalRule axiomEquality isect_memberEquality because_Cache equalityTransitivity equalitySymmetry intEquality

Latex:
\mforall{}[m1,n1,m2,n2:\mBbbZ{}].    \{m1..n1\msupminus{}\}  \msubseteq{}r  \{m2..n2\msupminus{}\}  supposing  (m2  \mleq{}  m1)  \mwedge{}  (n1  \mleq{}  n2)

Date html generated: 2016_05_13-PM-04_02_02
Last ObjectModification: 2015_12_26-AM-10_56_47

Theory : int_1

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