Nuprl Lemma : replace-seq-from-member-enum
∀f:ℕ ⟶ 𝔹. ∀m:ℕ. (replace-seq-from(f;m;tt) ∈ enum-fin-seq(m))
Proof
Definitions occuring in Statement :
replace-seq-from: replace-seq-from(s;n;k),
enum-fin-seq: enum-fin-seq(m),
l_member: (x ∈ l),
nat: ℕ,
btrue: tt,
bool: 𝔹,
all: ∀x:A. B[x],
function: x:A ⟶ B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
and: P ∧ Q,
subtype_rel: A ⊆r B,
list_n: A List(n),
so_lambda: λ2x.t[x],
so_apply: x[s],
enum-fin-seq: enum-fin-seq(m),
replace-seq-from: replace-seq-from(s;n;k),
less_than: a < b,
less_than': less_than'(a;b),
true: True,
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ge: i ≥ j ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
cand: A c∧ B,
nequal: a ≠ b ∈ T
Lemmas referenced :
l_member_wf,
nat_wf,
bool_wf,
replace-seq-from_wf,
decidable__le,
subtract_wf,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
le_wf,
btrue_wf,
enum-fin-seq_wf,
list_n_wf,
exp_wf2,
set_wf,
less_than_wf,
primrec-wf2,
primrec0_lemma,
member_singleton,
top_wf,
lt_int_wf,
eqtt_to_assert,
assert_of_lt_int,
nat_properties,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
primrec-unroll,
squash_wf,
true_wf,
list_wf,
replace-seq-from-succ,
append_wf,
map_wf,
bfalse_wf,
subtype_rel_self,
iff_weakening_equal,
bool_cases,
implies_l_member_append,
eq_int_wf,
assert_of_eq_int,
iff_imp_equal_bool,
assert_wf,
int_subtype_base,
neg_assert_of_eq_int,
member-map,
assert_elim,
btrue_neq_bfalse,
false_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
rename,
setElimination,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
functionEquality,
hypothesis,
functionExtensionality,
applyEquality,
hypothesisEquality,
because_Cache,
dependent_set_memberEquality,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
lessCases,
baseClosed,
equalityTransitivity,
equalitySymmetry,
imageMemberEquality,
isect_memberFormation,
axiomSqEquality,
imageElimination,
productElimination,
equalityElimination,
promote_hyp,
instantiate,
cumulativity,
universeEquality,
inlFormation,
int_eqReduceTrueSq,
int_eqReduceFalseSq,
productEquality,
inrFormation,
addLevel,
levelHypothesis
Latex:
\mforall{}f:\mBbbN{} {}\mrightarrow{} \mBbbB{}. \mforall{}m:\mBbbN{}. (replace-seq-from(f;m;tt) \mmember{} enum-fin-seq(m))
Date html generated:
2019_06_20-PM-02_57_15
Last ObjectModification:
2018_08_20-PM-09_39_30
Theory : continuity
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