Nuprl Lemma : length_sublist
∀[T:Type]. ∀[L1,L2:T List]. ||L1|| ≤ ||L2|| supposing L1 ⊆ L2
Proof
Definitions occuring in Statement :
sublist: L1 ⊆ L2,
length: ||as||,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
universe: Type
Definitions unfolded in proof :
sublist: L1 ⊆ L2,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
exists: ∃x:A. B[x],
and: P ∧ Q,
le: A ≤ B,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
subtype_rel: A ⊆r B,
int_seg: {i..j-},
all: ∀x:A. B[x],
guard: {T},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
less_than: a < b,
squash: ↓T,
ge: i ≥ j ,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
less_than'_wf,
length_wf,
int_seg_wf,
increasing_wf,
length_wf_nat,
equal_wf,
select_wf,
int_seg_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_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_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
non_neg_length,
lelt_wf,
nat_properties,
exists_wf,
all_wf,
list_wf,
increasing_le
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
hypothesisEquality,
because_Cache,
extract_by_obid,
isectElimination,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :productIsType,
Error :functionIsType,
Error :universeIsType,
natural_numberEquality,
functionExtensionality,
applyEquality,
setElimination,
rename,
cumulativity,
independent_isectElimination,
unionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
imageElimination,
dependent_set_memberEquality,
applyLambdaEquality,
functionEquality,
productEquality,
Error :inhabitedIsType,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L1,L2:T List]. ||L1|| \mleq{} ||L2|| supposing L1 \msubseteq{} L2
Date html generated:
2019_06_20-PM-01_22_19
Last ObjectModification:
2018_09_26-PM-05_20_50
Theory : list_1
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