Nuprl Lemma : listp_decomp
∀[T:Type]. ∀L:T List+. ∃x:T. ∃K:T List. (L = (K @ [x]) ∈ (T List))
Proof
Definitions occuring in Statement :
listp: A List+,
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
listp: A List+,
uimplies: b supposing a,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
and: P ∧ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ
Lemmas referenced :
listp_wf,
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformle_wf,
itermVar_wf,
itermConstant_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
length_wf,
decidable__lt,
list_decomp_reverse,
listp_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
dependent_functionElimination,
independent_isectElimination,
natural_numberEquality,
unionElimination,
productElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L:T List\msupplus{}. \mexists{}x:T. \mexists{}K:T List. (L = (K @ [x]))
Date html generated:
2016_05_14-PM-03_00_36
Last ObjectModification:
2016_01_15-AM-07_23_28
Theory : list_1
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