### Nuprl Lemma : interleaving_implies_occurence

`∀[T:Type]`
`  ∀L1,L2,L:T List.`
`    (interleaving(T;L1;L2;L) `` (∃f1:ℕ||L1|| ⟶ ℕ||L||. ∃f2:ℕ||L2|| ⟶ ℕ||L||. interleaving_occurence(T;L1;L2;L;f1;f2)))`

Proof

Definitions occuring in Statement :  interleaving_occurence: `interleaving_occurence(T;L1;L2;L;f1;f2)` interleaving: `interleaving(T;L1;L2;L)` length: `||as||` list: `T List` int_seg: `{i..j-}` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` exists: `∃x:A. B[x]` implies: `P `` Q` function: `x:A ⟶ B[x]` natural_number: `\$n` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` implies: `P `` Q` interleaving: `interleaving(T;L1;L2;L)` interleaving_occurence: `interleaving_occurence(T;L1;L2;L;f1;f2)` disjoint_sublists: `disjoint_sublists(T;L1;L2;L)` and: `P ∧ Q` exists: `∃x:A. B[x]` member: `t ∈ T` true: `True` prop: `ℙ` subtype_rel: `A ⊆r B` int_seg: `{i..j-}` so_lambda: `λ2x.t[x]` uimplies: `b supposing a` guard: `{T}` nat: `ℕ` lelt: `i ≤ j < k` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` false: `False` not: `¬A` top: `Top` less_than: `a < b` squash: `↓T` le: `A ≤ B` so_apply: `x[s]`
Lemmas referenced :  equal_wf nat_wf increasing_wf length_wf_nat int_seg_wf length_wf all_wf select_wf int_seg_properties nat_properties decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermVar_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_wf decidable__lt intformless_wf int_formula_prop_less_lemma non_neg_length lelt_wf not_wf exists_wf interleaving_wf list_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation lambdaFormation sqequalHypSubstitution sqequalRule productElimination thin dependent_pairFormation hypothesisEquality cut natural_numberEquality independent_pairFormation hypothesis productEquality introduction extract_by_obid isectElimination equalityTransitivity equalitySymmetry cumulativity functionExtensionality applyEquality lambdaEquality setElimination rename because_Cache independent_isectElimination applyLambdaEquality dependent_functionElimination unionElimination int_eqEquality intEquality isect_memberEquality voidElimination voidEquality computeAll imageElimination dependent_set_memberEquality independent_functionElimination functionEquality universeEquality

Latex:
\mforall{}[T:Type]
\mforall{}L1,L2,L:T  List.
(interleaving(T;L1;L2;L)
{}\mRightarrow{}  (\mexists{}f1:\mBbbN{}||L1||  {}\mrightarrow{}  \mBbbN{}||L||.  \mexists{}f2:\mBbbN{}||L2||  {}\mrightarrow{}  \mBbbN{}||L||.  interleaving\_occurence(T;L1;L2;L;f1;f2)))

Date html generated: 2017_10_01-AM-08_37_21
Last ObjectModification: 2017_07_26-PM-04_26_29

Theory : list!

Home Index