Nuprl Lemma : null-length-zero
∀[L:Top List]. null(L) = (||L|| =z 0)
Proof
Definitions occuring in Statement :
length: ||as||,
null: null(as),
list: T List,
eq_int: (i =z j),
bool: 𝔹,
uall: ∀[x:A]. B[x],
top: Top,
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
or: P ∨ Q,
eq_int: (i =z j),
cons: [a / b],
top: Top,
squash: ↓T,
prop: ℙ,
uimplies: b supposing a,
ge: i ≥ j ,
nequal: a ≠ b ∈ T ,
not: ¬A,
implies: P ⇒ Q,
le: A ≤ B,
and: P ∧ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
top_wf,
list-cases,
null_nil_lemma,
length_of_nil_lemma,
btrue_wf,
product_subtype_list,
null_cons_lemma,
length_of_cons_lemma,
equal_wf,
squash_wf,
true_wf,
bool_wf,
bfalse_wf,
eq_int_eq_false,
length_wf,
non_neg_length,
satisfiable-full-omega-tt,
intformand_wf,
intformeq_wf,
itermAdd_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
equal-wf-T-base,
iff_weakening_equal,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
unionElimination,
sqequalRule,
promote_hyp,
hypothesis_subsumption,
productElimination,
isect_memberEquality,
voidElimination,
voidEquality,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
addEquality,
natural_numberEquality,
independent_isectElimination,
lambdaFormation,
dependent_pairFormation,
int_eqEquality,
intEquality,
independent_pairFormation,
computeAll,
baseClosed,
imageMemberEquality,
independent_functionElimination,
because_Cache
Latex:
\mforall{}[L:Top List]. null(L) = (||L|| =\msubz{} 0)
Date html generated:
2017_04_17-AM-07_36_17
Last ObjectModification:
2017_02_27-PM-04_10_17
Theory : list_1
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