### Nuprl Lemma : list_decomp_reverse

`∀[T:Type]. ∀L:T List. ∃x:T. ∃L':T List. (L = (L' @ [x]) ∈ (T List)) supposing 0 < ||L||`

Proof

Definitions occuring in Statement :  length: `||as||` append: `as @ bs` cons: `[a / b]` nil: `[]` list: `T List` less_than: `a < b` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` exists: `∃x:A. B[x]` natural_number: `\$n` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` member: `t ∈ T` so_lambda: `λ2x.t[x]` uimplies: `b supposing a` prop: `ℙ` so_apply: `x[s]` implies: `P `` Q` less_than: `a < b` squash: `↓T` less_than': `less_than'(a;b)` false: `False` and: `P ∧ Q` top: `Top` or: `P ∨ Q` cons: `[a / b]` exists: `∃x:A. B[x]` append: `as @ bs` so_lambda: `so_lambda(x,y,z.t[x; y; z])` so_apply: `x[s1;s2;s3]` ge: `i ≥ j ` decidable: `Dec(P)` le: `A ≤ B` not: `¬A` satisfiable_int_formula: `satisfiable_int_formula(fmla)` true: `True`
Lemmas referenced :  list_induction isect_wf less_than_wf length_wf exists_wf list_wf equal_wf append_wf cons_wf nil_wf length_of_nil_lemma member-less_than length_of_cons_lemma list-cases product_subtype_list list_ind_nil_lemma non_neg_length decidable__lt full-omega-unsat intformand_wf intformnot_wf intformless_wf itermConstant_wf itermAdd_wf itermVar_wf intformle_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_less_lemma int_term_value_constant_lemma int_term_value_add_lemma int_term_value_var_lemma int_formula_prop_le_lemma int_formula_prop_wf list_ind_cons_lemma squash_wf true_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  lambdaFormation cut thin introduction extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality sqequalRule lambdaEquality natural_numberEquality hypothesis independent_functionElimination imageElimination productElimination voidElimination because_Cache independent_isectElimination rename Error :universeIsType,  dependent_functionElimination isect_memberEquality voidEquality addEquality universeEquality unionElimination promote_hyp hypothesis_subsumption dependent_pairFormation approximateComputation int_eqEquality intEquality independent_pairFormation applyEquality equalityTransitivity equalitySymmetry imageMemberEquality baseClosed

Latex:
\mforall{}[T:Type].  \mforall{}L:T  List.  \mexists{}x:T.  \mexists{}L':T  List.  (L  =  (L'  @  [x]))  supposing  0  <  ||L||

Date html generated: 2019_06_20-PM-01_45_27
Last ObjectModification: 2018_09_26-PM-02_54_49

Theory : list_1

Home Index