Nuprl Lemma : trivial-mklist
∀[T:Type]. ∀[L:T List]. ∀[f:ℕ||L|| ⟶ T]. mklist(||L||;f) = L ∈ (T List) supposing ∀i:ℕ||L||. ((f i) = L[i] ∈ T)
Proof
Definitions occuring in Statement :
mklist: mklist(n;f),
select: L[n],
length: ||as||,
list: T List,
int_seg: {i..j-},
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
squash: ↓T,
prop: ℙ,
nat: ℕ,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
less_than: a < b,
so_apply: x[s]
Lemmas referenced :
list_extensionality,
mklist_wf,
length_wf_nat,
mklist_length,
length_wf,
equal_wf,
squash_wf,
true_wf,
mklist_select,
lelt_wf,
select_wf,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
subtype_rel_self,
iff_weakening_equal,
less_than_wf,
nat_wf,
all_wf,
int_seg_wf,
int_seg_properties,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
lambdaFormation,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
because_Cache,
setElimination,
rename,
dependent_set_memberEquality,
independent_pairFormation,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
imageMemberEquality,
baseClosed,
instantiate,
productElimination,
functionExtensionality,
cumulativity,
axiomEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[f:\mBbbN{}||L|| {}\mrightarrow{} T]. mklist(||L||;f) = L supposing \mforall{}i:\mBbbN{}||L||. ((f i) = L[i])
Date html generated:
2018_05_21-PM-00_38_05
Last ObjectModification:
2018_05_19-AM-06_44_25
Theory : list_1
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