Nuprl Lemma : length_disjoint_sublists
∀[T:Type]. ∀[L1,L2,L:T List]. (||L1|| + ||L2||) ≤ ||L|| supposing disjoint_sublists(T;L1;L2;L)
Proof
Definitions occuring in Statement :
disjoint_sublists: disjoint_sublists(T;L1;L2;L),
length: ||as||,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
add: n + m,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
top: Top,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
uiff: uiff(P;Q),
or: P ∨ Q,
decidable: Dec(P),
ge: i ≥ j ,
guard: {T},
all: ∀x:A. B[x],
nat: ℕ
Lemmas referenced :
less_than'_wf,
length_wf,
disjoint_sublists_wf,
list_wf,
le_wf,
equal_wf,
false_wf,
int_formula_prop_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformeq_wf,
itermAdd_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
add-is-int-iff,
decidable__le,
nat_properties,
nat_wf,
length_wf_nat,
add_nat_wf,
injection_le,
disjoint_sublists_witness,
inject_wf,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
hypothesisEquality,
because_Cache,
extract_by_obid,
isectElimination,
hypothesis,
addEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality,
inhabitedIsType,
voidElimination,
universeEquality,
independent_functionElimination,
computeAll,
independent_pairFormation,
voidEquality,
intEquality,
int_eqEquality,
dependent_pairFormation,
independent_isectElimination,
baseClosed,
closedConclusion,
baseApply,
promote_hyp,
pointwiseFunctionality,
unionElimination,
natural_numberEquality,
rename,
setElimination,
applyLambdaEquality,
lambdaFormation,
cumulativity,
dependent_set_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L1,L2,L:T List]. (||L1|| + ||L2||) \mleq{} ||L|| supposing disjoint\_sublists(T;L1;L2;L)
Date html generated:
2019_10_15-AM-10_55_15
Last ObjectModification:
2018_09_27-AM-10_43_58
Theory : list!
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