Nuprl Lemma : cons_sublist_nil
∀[T:Type]. ∀x:T. ∀L:T List. ([x / L] ⊆ [] ⇐⇒ False)
Proof
Definitions occuring in Statement :
sublist: L1 ⊆ L2,
cons: [a / b],
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
false: False,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
false: False,
member: t ∈ T,
uimplies: b supposing a,
top: Top,
ge: i ≥ j ,
le: A ≤ B,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
length_sublist,
cons_wf,
nil_wf,
length_of_cons_lemma,
length_of_nil_lemma,
non_neg_length,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
itermAdd_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_wf,
sublist_wf,
false_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
hypothesis,
independent_isectElimination,
sqequalRule,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
productElimination,
natural_numberEquality,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}x:T. \mforall{}L:T List. ([x / L] \msubseteq{} [] \mLeftarrow{}{}\mRightarrow{} False)
Date html generated:
2018_05_21-PM-00_33_11
Last ObjectModification:
2018_05_19-AM-06_42_50
Theory : list_1
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