### Nuprl Lemma : iseg_select2

`∀[T:Type]. ∀[l1,l2:T List].  {∀[i:ℕ||l1||]. (l1[i] = l2[i] ∈ T)} supposing l1 ≤ l2`

Proof

Definitions occuring in Statement :  iseg: `l1 ≤ l2` select: `L[n]` length: `||as||` list: `T List` int_seg: `{i..j-}` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` guard: `{T}` natural_number: `\$n` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  guard: `{T}` uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` all: `∀x:A. B[x]` iff: `P `⇐⇒` Q` and: `P ∧ Q` implies: `P `` Q` cand: `A c∧ B` subtype_rel: `A ⊆r B` le: `A ≤ B` less_than': `less_than'(a;b)` false: `False` not: `¬A` prop: `ℙ` int_seg: `{i..j-}` lelt: `i ≤ j < k` decidable: `Dec(P)` or: `P ∨ Q` less_than: `a < b` squash: `↓T` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` top: `Top`
Lemmas referenced :  iseg_wf int_seg_wf int_formula_prop_wf int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_not_lemma int_formula_prop_and_lemma itermVar_wf intformless_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__lt int_seg_properties false_wf length_wf int_seg_subtype_nat iseg_select
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality dependent_functionElimination productElimination independent_functionElimination hypothesis applyEquality natural_numberEquality independent_isectElimination independent_pairFormation lambdaFormation setElimination rename unionElimination imageElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality computeAll axiomEquality because_Cache equalityTransitivity equalitySymmetry

Latex:
\mforall{}[T:Type].  \mforall{}[l1,l2:T  List].    \{\mforall{}[i:\mBbbN{}||l1||].  (l1[i]  =  l2[i])\}  supposing  l1  \mleq{}  l2

Date html generated: 2016_05_14-PM-01_34_28
Last ObjectModification: 2016_01_15-AM-08_26_00

Theory : list_1

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