### Nuprl Lemma : int_seg_subtype_nat

`∀[a,b:ℤ].  {a..b-} ⊆r ℕ supposing 0 ≤ a`

Proof

Definitions occuring in Statement :  int_seg: `{i..j-}` nat: `ℕ` uimplies: `b supposing a` subtype_rel: `A ⊆r B` uall: `∀[x:A]. B[x]` le: `A ≤ B` natural_number: `\$n` int: `ℤ`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` int_seg: `{i..j-}` nat: `ℕ` so_lambda: `λ2x.t[x]` lelt: `i ≤ j < k` so_apply: `x[s]` subtype_rel: `A ⊆r B` and: `P ∧ Q` prop: `ℙ` all: `∀x:A. B[x]` implies: `P `` Q` le: `A ≤ B` guard: `{T}`
Lemmas referenced :  subtype_rel_sets and_wf le_wf less_than_wf le_transitivity
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin intEquality because_Cache lambdaEquality hypothesisEquality hypothesis natural_numberEquality independent_isectElimination setElimination rename setEquality lambdaFormation productElimination axiomEquality isect_memberEquality equalityTransitivity equalitySymmetry

Latex:
\mforall{}[a,b:\mBbbZ{}].    \{a..b\msupminus{}\}  \msubseteq{}r  \mBbbN{}  supposing  0  \mleq{}  a

Date html generated: 2016_05_13-PM-03_33_14
Last ObjectModification: 2015_12_26-AM-09_44_52

Theory : arithmetic

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