Nuprl Lemma : l_before_interleaving
∀[T:Type]. ∀L,L1,L2:T List. (interleaving(T;L1;L2;L) ⇒ {∀x,y:T. (x before y ∈ L1 ⇒ x before y ∈ L)})
Proof
Definitions occuring in Statement :
interleaving: interleaving(T;L1;L2;L),
l_before: x before y ∈ l,
list: T List,
uall: ∀[x:A]. B[x],
guard: {T},
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
guard: {T},
interleaving: interleaving(T;L1;L2;L),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
member: t ∈ T,
prop: ℙ,
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
false: False,
uiff: uiff(P;Q),
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top
Lemmas referenced :
l_before_wf,
equal_wf,
nat_wf,
length_wf_nat,
length_wf,
add_nat_wf,
nat_properties,
decidable__le,
add-is-int-iff,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
itermAdd_wf,
intformeq_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_wf,
false_wf,
le_wf,
disjoint_sublists_wf,
list_wf,
l_before_sublist,
disjoint_sublists_sublist
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
introduction,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
hypothesis,
productEquality,
dependent_set_memberEquality,
addEquality,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
setElimination,
rename,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
pointwiseFunctionality,
promote_hyp,
baseApply,
closedConclusion,
baseClosed,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]
\mforall{}L,L1,L2:T List. (interleaving(T;L1;L2;L) {}\mRightarrow{} \{\mforall{}x,y:T. (x before y \mmember{} L1 {}\mRightarrow{} x before y \mmember{} L)\})
Date html generated:
2017_10_01-AM-08_35_50
Last ObjectModification:
2017_07_26-PM-04_25_59
Theory : list!
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