Nuprl Lemma : iseg_is_sublist
∀[T:Type]. ∀L_1,L_2:T List. (L_1 ≤ L_2 ⇒ L_1 ⊆ L_2)
Proof
Definitions occuring in Statement :
iseg: l1 ≤ l2,
sublist: L1 ⊆ L2,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
sublist: L1 ⊆ L2,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uimplies: b supposing a,
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
int_seg: {i..j-},
lelt: i ≤ j < k,
rev_implies: P ⇐ Q,
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
le: A ≤ B,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top,
prop: ℙ,
cand: A c∧ B,
subtype_rel: A ⊆r B,
less_than': less_than'(a;b),
guard: {T},
so_lambda: λ2x.t[x],
ge: i ≥ j ,
nat: ℕ,
so_apply: x[s]
Lemmas referenced :
iseg_length,
iseg_select,
decidable__lt,
length_wf,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformless_wf,
itermVar_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
lelt_wf,
int_seg_wf,
id_increasing,
length_wf_nat,
int_seg_subtype_nat,
false_wf,
int_seg_properties,
increasing_wf,
all_wf,
equal_wf,
select_wf,
decidable__le,
itermConstant_wf,
int_term_value_constant_lemma,
non_neg_length,
nat_properties,
iseg_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
because_Cache,
dependent_functionElimination,
dependent_pairFormation,
productElimination,
lambdaEquality,
setElimination,
rename,
dependent_set_memberEquality,
independent_pairFormation,
unionElimination,
imageElimination,
natural_numberEquality,
approximateComputation,
independent_functionElimination,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
cumulativity,
applyEquality,
productEquality,
functionExtensionality,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L$_{1}$,L$_{2}$:T List. (L$_{1}\000C$ \mleq{} L$_{2}$ {}\mRightarrow{} L$_{1}$ \msubseteq{} L$_{2}$)
Date html generated:
2018_05_21-PM-00_36_31
Last ObjectModification:
2018_05_19-AM-06_43_37
Theory : list_1
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