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
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