Nuprl Lemma : l_contains-firstn
∀[T:Type]. ∀L:T List. ∀n:ℕ. firstn(n;L) ⊆ L
Proof
Definitions occuring in Statement :
l_contains: A ⊆ B,
firstn: firstn(n;as),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
l_contains: A ⊆ B,
l_all: (∀x∈L.P[x]),
member: t ∈ T,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
int_iseg: {i...j},
and: P ∧ Q,
cand: A c∧ B,
guard: {T},
int_seg: {i..j-},
ge: i ≥ j ,
lelt: i ≤ j < k,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
le: A ≤ B,
less_than': less_than'(a;b),
less_than: a < b
Lemmas referenced :
top_wf,
subtype_rel_list,
firstn_all,
false_wf,
int_seg_subtype,
select_member,
iff_weakening_equal,
int_formula_prop_less_lemma,
intformless_wf,
select_firstn,
true_wf,
squash_wf,
l_member_wf,
le_wf,
and_wf,
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,
nat_properties,
int_seg_properties,
length_firstn,
decidable__le,
list_wf,
nat_wf,
firstn_wf,
length_wf,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesisEquality,
setElimination,
rename,
hypothesis,
universeEquality,
dependent_functionElimination,
unionElimination,
sqequalRule,
dependent_set_memberEquality,
productElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
because_Cache,
imageMemberEquality,
baseClosed,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. \mforall{}n:\mBbbN{}. firstn(n;L) \msubseteq{} L
Date html generated:
2016_05_14-PM-02_08_53
Last ObjectModification:
2016_01_15-AM-08_02_52
Theory : list_1
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