Nuprl Lemma : sublist_nil
∀[T:Type]. ∀L:T List. (L ⊆ [] ⇐⇒ L = [] ∈ (T List))
Proof
Definitions occuring in Statement :
sublist: L1 ⊆ L2,
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top
Lemmas referenced :
sublist_wf,
nil_wf,
equal-wf-T-base,
list_wf,
length_zero,
length_sublist,
length_of_nil_lemma,
non_neg_length,
decidable__equal_int,
length_wf,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
nil-sublist
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
cut,
hypothesis,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
baseClosed,
universeEquality,
productElimination,
independent_isectElimination,
because_Cache,
sqequalRule,
dependent_functionElimination,
unionElimination,
natural_numberEquality,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
hyp_replacement,
equalitySymmetry,
Error :applyLambdaEquality
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. (L \msubseteq{} [] \mLeftarrow{}{}\mRightarrow{} L = [])
Date html generated:
2016_10_21-AM-10_02_01
Last ObjectModification:
2016_07_12-AM-05_23_43
Theory : list_1
Home
Index