Nuprl Lemma : length_interleaving
∀[T:Type]. ∀[L,L1,L2:T List].  ||L|| = (||L1|| + ||L2||) ∈ ℕ supposing interleaving(T;L1;L2;L)
Proof
Definitions occuring in Statement : 
interleaving: interleaving(T;L1;L2;L)
, 
length: ||as||
, 
list: T List
, 
nat: ℕ
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
add: n + m
, 
universe: Type
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
interleaving: interleaving(T;L1;L2;L)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
and: P ∧ Q
, 
prop: ℙ
, 
nat: ℕ
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
guard: {T}
, 
ge: i ≥ j 
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
false: False
, 
uiff: uiff(P;Q)
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
not: ¬A
, 
top: Top
Lemmas referenced : 
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
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
introduction, 
cut, 
sqequalHypSubstitution, 
productElimination, 
thin, 
hypothesis, 
productEquality, 
extract_by_obid, 
isectElimination, 
cumulativity, 
hypothesisEquality, 
dependent_set_memberEquality, 
addEquality, 
lambdaFormation, 
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, 
axiomEquality, 
universeEquality
Latex:
\mforall{}[T:Type].  \mforall{}[L,L1,L2:T  List].    ||L||  =  (||L1||  +  ||L2||)  supposing  interleaving(T;L1;L2;L)
Date html generated:
2017_10_01-AM-08_36_13
Last ObjectModification:
2017_07_26-PM-04_26_07
Theory : list!
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