Nuprl Lemma : hd-append
∀[T:Type]. ∀[L1:T List+]. ∀[L2:T List]. (hd(L1 @ L2) = hd(L1) ∈ T)
Proof
Definitions occuring in Statement :
listp: A List+,
hd: hd(l),
append: as @ bs,
list: T List,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
listp: A List+,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
squash: ↓T,
prop: ℙ,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
sq_type: SQType(T),
select: L[n]
Lemmas referenced :
select-as-hd,
append_wf,
subtype_rel_list,
top_wf,
listp_properties,
equal_wf,
squash_wf,
true_wf,
select_append,
false_wf,
non_neg_length,
decidable__lt,
length_wf,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
lelt_wf,
select_wf,
iff_weakening_equal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
iff_imp_equal_bool,
lt_int_wf,
btrue_wf,
less_than_wf,
assert_of_lt_int,
assert_wf,
iff_wf,
list_wf,
listp_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
setElimination,
rename,
because_Cache,
hypothesis,
applyEquality,
independent_isectElimination,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
dependent_functionElimination,
addEquality,
unionElimination,
productElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
computeAll,
imageMemberEquality,
baseClosed,
universeEquality,
independent_functionElimination,
instantiate,
addLevel,
impliesFunctionality,
axiomEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L1:T List\msupplus{}]. \mforall{}[L2:T List]. (hd(L1 @ L2) = hd(L1))
Date html generated:
2017_04_17-AM-08_48_09
Last ObjectModification:
2017_02_27-PM-05_06_53
Theory : list_1
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