Nuprl Lemma : seq-add-same
∀[f:ℕ ⟶ ℕ]. ∀[n:ℕ]. (f.f n@n = f ∈ (ℕ ⟶ ℕ))
Proof
Definitions occuring in Statement :
seq-add: s.x@n,
nat: ℕ,
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ⟶ B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
seq-add: s.x@n,
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
ge: i ≥ j ,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
bfalse: ff,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
nequal: a ≠ b ∈ T
Lemmas referenced :
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
subtype_base_sq,
int_subtype_base,
nat_properties,
decidable__equal_nat,
nat_wf,
le_wf,
satisfiable-full-omega-tt,
intformnot_wf,
intformeq_wf,
itermVar_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
equal_wf,
int_formula_prop_wf,
eqff_to_assert,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
functionExtensionality,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
int_eqReduceTrueSq,
promote_hyp,
instantiate,
cumulativity,
intEquality,
dependent_functionElimination,
independent_functionElimination,
applyEquality,
dependent_set_memberEquality,
natural_numberEquality,
because_Cache,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
int_eqReduceFalseSq,
axiomEquality,
functionEquality
Latex:
\mforall{}[f:\mBbbN{} {}\mrightarrow{} \mBbbN{}]. \mforall{}[n:\mBbbN{}]. (f.f n@n = f)
Date html generated:
2017_04_20-AM-07_21_54
Last ObjectModification:
2017_02_27-PM-05_56_48
Theory : continuity
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