Nuprl Lemma : functions-list-0
∀[b:ℕ]. (functions-list(0;b) = [λx.x] ∈ ((ℕ0 ⟶ ℕb) List))
Proof
Definitions occuring in Statement :
functions-list: functions-list(n;b),
cons: [a / b],
nil: [],
list: T List,
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
function: x:A ⟶ B[x],
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
top: Top,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
uimplies: b supposing a,
ge: i ≥ j ,
lelt: i ≤ j < k,
int_seg: {i..j-},
all: ∀x:A. B[x],
so_apply: x[s],
so_lambda: λ2x.t[x],
prop: ℙ,
implies: P ⇒ Q,
not: ¬A,
false: False,
less_than': less_than'(a;b),
and: P ∧ Q,
le: A ≤ B,
nat: ℕ,
member: t ∈ T,
uall: ∀[x:A]. B[x],
true: True,
decidable: Dec(P),
subtype_rel: A ⊆r B,
guard: {T},
squash: ↓T,
cons: [a / b],
or: P ∨ Q,
subtract: n - m,
select: L[n],
no_repeats: no_repeats(T;l),
less_than: a < b,
nat_plus: ℕ+
Lemmas referenced :
nat_wf,
equal_wf,
lelt_wf,
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_and_lemma,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
intformand_wf,
full-omega-unsat,
nat_properties,
l_member_wf,
all_wf,
no_repeats_wf,
int_seg_wf,
list_wf,
set_wf,
le_wf,
false_wf,
functions-list_wf,
decidable__equal_int,
int_seg_properties,
cons_wf,
product_subtype_list,
btrue_neq_bfalse,
nil_wf,
member-implies-null-eq-bfalse,
btrue_wf,
null_nil_lemma,
list-cases,
length_of_cons_lemma,
equal-wf-base,
int_formula_prop_eq_lemma,
intformeq_wf,
decidable__lt,
nat_plus_properties,
nat_plus_wf,
less_than_wf,
int_term_value_add_lemma,
int_formula_prop_not_lemma,
itermAdd_wf,
intformnot_wf,
decidable__le,
non_neg_length,
length_wf,
add_nat_plus
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
voidEquality,
voidElimination,
isect_memberEquality,
intEquality,
int_eqEquality,
dependent_pairFormation,
independent_functionElimination,
approximateComputation,
independent_isectElimination,
dependent_functionElimination,
productElimination,
applyEquality,
functionExtensionality,
productEquality,
lambdaEquality,
rename,
setElimination,
because_Cache,
functionEquality,
hypothesisEquality,
hypothesis,
lambdaFormation,
independent_pairFormation,
sqequalRule,
natural_numberEquality,
dependent_set_memberEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
baseClosed,
imageMemberEquality,
imageElimination,
hypothesis_subsumption,
promote_hyp,
unionElimination,
pointwiseFunctionality,
applyLambdaEquality,
addEquality
Latex:
\mforall{}[b:\mBbbN{}]. (functions-list(0;b) = [\mlambda{}x.x])
Date html generated:
2018_05_21-PM-08_25_09
Last ObjectModification:
2017_12_14-PM-06_48_15
Theory : general
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