Nuprl Lemma : firstn-iseg
∀[T:Type]. ∀L:T List. ∀n:ℕ. firstn(n;L) ≤ L
Proof
Definitions occuring in Statement :
iseg: l1 ≤ l2,
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],
member: t ∈ T,
so_lambda: λ2x.t[x],
nat: ℕ,
so_apply: x[s],
implies: P ⇒ Q,
prop: ℙ,
firstn: firstn(n;as),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
cand: A c∧ B,
ge: i ≥ j ,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
list_induction,
all_wf,
nat_wf,
iseg_wf,
firstn_wf,
list_wf,
list_ind_nil_lemma,
nil_iseg,
nil_wf,
list_ind_cons_lemma,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
less_than_wf,
cons_wf,
subtract_wf,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
le_wf,
cons_iseg
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
hypothesis,
cumulativity,
setElimination,
rename,
independent_functionElimination,
because_Cache,
dependent_functionElimination,
universeEquality,
isect_memberEquality,
voidElimination,
voidEquality,
natural_numberEquality,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
dependent_pairFormation,
promote_hyp,
instantiate,
independent_pairFormation,
dependent_set_memberEquality,
int_eqEquality,
intEquality,
computeAll
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. \mforall{}n:\mBbbN{}. firstn(n;L) \mleq{} L
Date html generated:
2017_04_17-AM-08_01_52
Last ObjectModification:
2017_02_27-PM-04_32_00
Theory : list_1
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