Nuprl Lemma : sublist_weakening
∀[T:Type]. ∀L1,L2:T List. L1 ⊆ L2 supposing L1 = L2 ∈ (T List)
Proof
Definitions occuring in Statement :
sublist: L1 ⊆ L2,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
sublist: L1 ⊆ L2,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
exists: ∃x:A. B[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
prop: ℙ,
nat: ℕ,
le: A ≤ B,
less_than: a < b,
cand: A c∧ B,
squash: ↓T,
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
ge: i ≥ j ,
so_apply: x[s]
Lemmas referenced :
and_wf,
equal_wf,
list_wf,
length_wf_nat,
nat_wf,
less_than_wf,
lelt_wf,
length_wf,
int_seg_wf,
id_increasing,
select_wf,
int_seg_properties,
decidable__le,
satisfiable-full-omega-tt,
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,
increasing_wf,
all_wf,
non_neg_length,
nat_properties,
set_wf,
le_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
axiomEquality,
hypothesis,
thin,
rename,
dependent_pairFormation,
lambdaEquality,
sqequalHypSubstitution,
setElimination,
dependent_set_memberEquality,
hypothesisEquality,
productElimination,
independent_pairFormation,
extract_by_obid,
isectElimination,
applyEquality,
setEquality,
equalityTransitivity,
equalitySymmetry,
hyp_replacement,
Error :applyLambdaEquality,
cumulativity,
natural_numberEquality,
imageElimination,
because_Cache,
independent_isectElimination,
dependent_functionElimination,
unionElimination,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
imageMemberEquality,
baseClosed,
productEquality,
functionExtensionality,
independent_functionElimination,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L1,L2:T List. L1 \msubseteq{} L2 supposing L1 = L2
Date html generated:
2016_10_21-AM-10_01_56
Last ObjectModification:
2016_07_12-AM-05_24_09
Theory : list_1
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