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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