Nuprl Lemma : sublist_wf
∀[T:Type]. ∀[L1,L2:T List]. (L1 ⊆ L2 ∈ ℙ)
Proof
Definitions occuring in Statement :
sublist: L1 ⊆ L2,
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
sublist: L1 ⊆ L2,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
less_than: a < b,
squash: ↓T,
ge: i ≥ j ,
nat: ℕ
Lemmas referenced :
list_wf,
le_wf,
nat_properties,
lelt_wf,
non_neg_length,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
int_formula_prop_wf,
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,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
int_seg_properties,
select_wf,
equal_wf,
all_wf,
subtype_rel_dep_function,
length_wf_nat,
increasing_wf,
length_wf,
int_seg_wf,
exists_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
natural_numberEquality,
cumulativity,
hypothesisEquality,
hypothesis,
because_Cache,
lambdaEquality,
productEquality,
applyEquality,
intEquality,
independent_isectElimination,
lambdaFormation,
setElimination,
rename,
productElimination,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
imageElimination,
dependent_set_memberEquality,
equalityTransitivity,
equalitySymmetry,
setEquality,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L1,L2:T List]. (L1 \msubseteq{} L2 \mmember{} \mBbbP{})
Date html generated:
2016_05_14-AM-07_42_56
Last ObjectModification:
2016_01_15-AM-08_35_23
Theory : list_1
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