Nuprl Lemma : radd-list-one
∀[L:Top List]. (radd-list(map(λk.r1;L)) = r(||L||))
Proof
Definitions occuring in Statement :
req: x = y,
radd-list: radd-list(L),
int-to-real: r(n),
length: ||as||,
map: map(f;as),
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
lambda: λx.A[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
so_apply: x[s],
implies: P ⇒ Q,
all: ∀x:A. B[x],
top: Top,
prop: ℙ,
listp: A List+,
uiff: uiff(P;Q),
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
list_induction,
top_wf,
req_wf,
radd-list_wf-bag,
map_wf_bag,
real_wf,
int-to-real_wf,
list-subtype-bag,
length_wf,
list_wf,
map_nil_lemma,
length_of_nil_lemma,
radd_list_nil_lemma,
req_weakening,
map_cons_lemma,
length_of_cons_lemma,
req_witness,
cons_wf_listp,
map_wf,
subtype_rel_set,
bag_wf,
less_than_wf,
radd_wf,
req-int,
decidable__equal_int,
satisfiable-full-omega-tt,
intformnot_wf,
intformeq_wf,
itermAdd_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
uiff_transitivity,
req_functionality,
req_transitivity,
radd-list-cons,
radd_functionality,
radd-int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesis,
sqequalRule,
lambdaEquality,
natural_numberEquality,
hypothesisEquality,
applyEquality,
because_Cache,
independent_isectElimination,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
lambdaFormation,
rename,
addEquality,
productElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
computeAll
Latex:
\mforall{}[L:Top List]. (radd-list(map(\mlambda{}k.r1;L)) = r(||L||))
Date html generated:
2017_10_02-PM-07_16_04
Last ObjectModification:
2017_07_28-AM-07_20_49
Theory : reals
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