Nuprl Lemma : mklist-general-fun
∀[T:Type]. ∀[h:(T List) ⟶ T]. ∀[n:ℕ]. (mklist-general(n;h) ~ map(λn.mklist-general(n + 1;h)[n];upto(n)))
Proof
Definitions occuring in Statement :
upto: upto(n),
mklist-general: mklist-general(n;h),
select: L[n],
map: map(f;as),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
int_seg: {i..j-},
so_lambda: λ2x.t[x],
so_apply: x[s],
upto: upto(n),
from-upto: [n, m),
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
bfalse: ff,
nil: [],
it: ⋅,
sq_type: SQType(T),
guard: {T},
mklist-general: mklist-general(n;h),
map: map(f;as),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
decidable: Dec(P),
or: P ∨ Q,
nat_plus: ℕ+,
last: last(L)
Lemmas referenced :
mklist-general_wf,
last_append_singleton,
le_wf,
mklist-general-length,
subtract-add-cancel,
map-upto,
mklist-general_add1,
list_wf,
nat_wf,
int_term_value_subtract_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
intformnot_wf,
subtract_wf,
decidable__le,
list_ind_nil_lemma,
primrec0_lemma,
int_seg_wf,
nil_wf,
int_subtype_base,
set_subtype_base,
list_subtype_base,
subtype_base_sq,
less_than_wf,
ge_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
independent_functionElimination,
sqequalAxiom,
instantiate,
because_Cache,
equalityTransitivity,
equalitySymmetry,
unionElimination,
functionEquality,
universeEquality,
baseClosed,
sqequalIntensionalEquality,
productElimination,
dependent_set_memberEquality,
cumulativity,
applyEquality
Latex:
\mforall{}[T:Type]. \mforall{}[h:(T List) {}\mrightarrow{} T]. \mforall{}[n:\mBbbN{}].
(mklist-general(n;h) \msim{} map(\mlambda{}n.mklist-general(n + 1;h)[n];upto(n)))
Date html generated:
2016_05_15-PM-04_35_45
Last ObjectModification:
2016_01_16-AM-11_17_45
Theory : general
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