Nuprl Lemma : length2-decomp
∀[T:Type]. ∀L:T List. ∃a,b:T. ∃L':T List. (L = (L' @ [a; b]) ∈ (T List)) supposing ||L|| ≥ 2
Proof
Definitions occuring in Statement :
length: ||as||,
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
ge: i ≥ j ,
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],
uimplies: b supposing a,
member: t ∈ T,
ge: i ≥ j ,
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
subtype_rel: A ⊆r B,
top: Top,
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
squash: ↓T,
int_iseg: {i...j},
cand: A c∧ B,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
sq_type: SQType(T),
cons: [a / b],
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
less_than'_wf,
length_wf,
append_firstn_lastn_sq,
subtype_rel_list,
top_wf,
subtract_wf,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_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_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
itermAdd_wf,
int_formula_prop_less_lemma,
int_term_value_add_lemma,
lelt_wf,
ge_wf,
list_wf,
equal_wf,
squash_wf,
true_wf,
length_nth_tl,
le_wf,
iff_weakening_equal,
decidable__equal_int,
intformeq_wf,
int_formula_prop_eq_lemma,
nth_tl_wf,
list-cases,
length_of_nil_lemma,
subtype_base_sq,
int_subtype_base,
false_wf,
equal-wf-base,
product_subtype_list,
length_of_cons_lemma,
cons_wf,
nil_wf,
exists_wf,
non_neg_length,
equal-wf-T-base,
firstn_wf,
append_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
hypothesisEquality,
voidElimination,
extract_by_obid,
isectElimination,
cumulativity,
hypothesis,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
rename,
applyEquality,
independent_isectElimination,
isect_memberEquality,
voidEquality,
because_Cache,
dependent_set_memberEquality,
independent_pairFormation,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
computeAll,
addEquality,
universeEquality,
imageElimination,
productEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination,
addLevel,
instantiate,
levelHypothesis,
promote_hyp,
hypothesis_subsumption
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. \mexists{}a,b:T. \mexists{}L':T List. (L = (L' @ [a; b])) supposing ||L|| \mgeq{} 2
Date html generated:
2017_04_17-AM-07_52_20
Last ObjectModification:
2017_02_27-PM-04_25_17
Theory : list_1
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