Nuprl Lemma : interleaving_of_nil
∀[T:Type]. ∀L1,L2:T List. (interleaving(T;L1;L2;[]) ⇐⇒ (L1 = [] ∈ (T List)) ∧ (L2 = [] ∈ (T List)))
Proof
Definitions occuring in Statement :
interleaving: interleaving(T;L1;L2;L),
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: 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,
uiff: uiff(P;Q),
uimplies: b supposing a,
ge: i ≥ j ,
nat: ℕ,
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
false: False,
le: A ≤ B,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
length_zero,
length_interleaving,
nil_wf,
length_of_nil_lemma,
non_neg_length,
nat_properties,
decidable__equal_int,
length_wf,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
itermAdd_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_term_value_add_lemma,
int_formula_prop_wf,
interleaving_wf,
equal-wf-T-base,
list_wf,
nil_interleaving
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation,
independent_pairFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productElimination,
independent_isectElimination,
because_Cache,
hypothesis,
sqequalRule,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
setElimination,
rename,
dependent_functionElimination,
unionElimination,
natural_numberEquality,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
productEquality,
baseClosed,
universeIsType,
universeEquality,
hyp_replacement
Latex:
\mforall{}[T:Type]. \mforall{}L1,L2:T List. (interleaving(T;L1;L2;[]) \mLeftarrow{}{}\mRightarrow{} (L1 = []) \mwedge{} (L2 = []))
Date html generated:
2019_10_15-AM-10_55_38
Last ObjectModification:
2018_09_27-AM-10_42_47
Theory : list!
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