Nuprl Lemma : length-zero-implies-nil
∀l:Base. l ~ [] supposing ||l|| = 0 ∈ ℤ
Proof
Definitions occuring in Statement :
length: ||as||,
nil: [],
uimplies: b supposing a,
all: ∀x:A. B[x],
natural_number: $n,
int: ℤ,
base: Base,
sqequal: s ~ t,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
sq_type: SQType(T),
guard: {T},
length: ||as||,
list_ind: list_ind,
has-value: (a)↓,
cons: [a / b],
label: ...$L... t,
ge: i ≥ j ,
nil: [],
it: ⋅
Lemmas referenced :
bottom_diverge,
has-value-implies-dec-isaxiom-2,
int_term_value_add_lemma,
itermAdd_wf,
nat_properties,
length-nat-if-has-value,
length_of_cons_lemma,
top_wf,
has-value-implies-dec-ispair-2,
base_wf,
equal-wf-base,
int_formula_prop_wf,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
int-value-type,
le_wf,
set-value-type,
nat_wf,
value-type-has-value,
subtype_rel_self,
subtype_base_sq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
independent_isectElimination,
hypothesis,
sqequalRule,
lambdaEquality,
natural_numberEquality,
hypothesisEquality,
intEquality,
dependent_set_memberEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
sqequalAxiom,
baseApply,
closedConclusion,
baseClosed,
callbyvalueCallbyvalue,
callbyvalueReduce,
callbyvalueAdd,
productElimination,
applyEquality,
setElimination,
rename,
setEquality
Latex:
\mforall{}l:Base. l \msim{} [] supposing ||l|| = 0
Date html generated:
2016_05_14-AM-07_42_11
Last ObjectModification:
2016_01_15-AM-08_35_36
Theory : list_1
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