Nuprl Lemma : whole_segment
∀T:Type. ∀as:T List. ((as[0..||as||-]) = as ∈ (T List))
Proof
Definitions occuring in Statement :
segment: as[m..n-],
length: ||as||,
list: T List,
all: ∀x:A. B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
segment: as[m..n-],
all: ∀x:A. B[x],
nth_tl: nth_tl(n;as),
le_int: i ≤z j,
lt_int: i <z j,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
prop: ℙ,
sq_type: SQType(T),
guard: {T},
subtype_rel: A ⊆r B
Lemmas referenced :
subtype_base_sq,
int_subtype_base,
decidable__equal_int,
length_wf,
full-omega-unsat,
intformnot_wf,
intformeq_wf,
itermSubtract_wf,
itermVar_wf,
itermConstant_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
firstn_all,
subtype_rel_list,
top_wf,
decidable__le,
intformle_wf,
int_formula_prop_le_lemma,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
hypothesis,
dependent_functionElimination,
because_Cache,
unionElimination,
hypothesisEquality,
natural_numberEquality,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
equalityTransitivity,
equalitySymmetry,
applyEquality,
universeEquality
Latex:
\mforall{}T:Type. \mforall{}as:T List. ((as[0..||as||\msupminus{}]) = as)
Date html generated:
2017_09_29-PM-05_58_11
Last ObjectModification:
2017_07_12-AM-11_48_18
Theory : list_1
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