Nuprl Lemma : map_length_nat
∀[A,B:Type]. ∀[f:A ⟶ B]. ∀[as:A List]. (||map(f;as)|| = ||as|| ∈ ℕ)
Proof
Definitions occuring in Statement :
length: ||as||,
map: map(f;as),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
all: ∀x:A. B[x],
top: Top,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
prop: ℙ,
false: False,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
not: ¬A,
guard: {T},
ge: i ≥ j
Lemmas referenced :
list_induction,
equal_wf,
nat_wf,
length_wf_nat,
map_wf,
list_wf,
map_nil_lemma,
length_of_nil_lemma,
decidable__equal_int,
satisfiable-full-omega-tt,
intformnot_wf,
intformeq_wf,
itermConstant_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
false_wf,
le_wf,
map_cons_lemma,
length_of_cons_lemma,
nat_properties,
length_wf,
intformand_wf,
itermAdd_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
add_nat_wf,
decidable__le,
intformle_wf,
int_formula_prop_le_lemma
Rules used in proof :
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
hypothesis,
cumulativity,
functionExtensionality,
applyEquality,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
natural_numberEquality,
because_Cache,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
intEquality,
computeAll,
dependent_set_memberEquality,
equalityTransitivity,
equalitySymmetry,
independent_pairFormation,
lambdaFormation,
rename,
applyLambdaEquality,
setElimination,
addEquality,
int_eqEquality,
functionEquality,
universeEquality,
isect_memberFormation,
axiomEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[as:A List]. (||map(f;as)|| = ||as||)
Date html generated:
2017_04_17-AM-08_44_32
Last ObjectModification:
2017_02_27-PM-05_02_02
Theory : list_1
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