Nuprl Lemma : map_wf_listp
∀[A,B:Type]. ∀[f:A ⟶ B]. ∀[l:A List+]. (map(f;l) ∈ B List+)
Proof
Definitions occuring in Statement :
listp: A List+,
map: map(f;as),
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
listp: A List+,
top: Top,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
and: P ∧ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
prop: ℙ
Lemmas referenced :
listp_wf,
map_wf,
map-length,
decidable__lt,
length_wf,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_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_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
less_than_wf,
listp_properties
Rules used in proof :
universeIsType,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
because_Cache,
functionIsType,
functionEquality,
inhabitedIsType,
universeEquality,
isect_memberFormation_alt,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
rename,
setElimination,
lemma_by_obid,
dependent_set_memberEquality,
voidElimination,
voidEquality,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
productElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
independent_pairFormation
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[l:A List\msupplus{}]. (map(f;l) \mmember{} B List\msupplus{})
Date html generated:
2019_10_15-AM-10_53_28
Last ObjectModification:
2018_09_27-AM-10_02_45
Theory : list!
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