Nuprl Lemma : length_upto
∀[n:ℕ]. (||upto(n)|| ~ n)
Proof
Definitions occuring in Statement :
upto: upto(n),
length: ||as||,
nat: ℕ,
uall: ∀[x:A]. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
upto: upto(n),
uall: ∀[x:A]. B[x],
member: t ∈ T,
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,
ifthenelse: if b then t else f fi ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
sq_type: SQType(T),
guard: {T},
bfalse: ff,
bnot: ¬bb,
assert: ↑b
Lemmas referenced :
nat_wf,
length-from-upto,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
subtype_base_sq,
int_subtype_base,
nat_properties,
decidable__equal_int,
satisfiable-full-omega-tt,
intformnot_wf,
intformeq_wf,
itermSubtract_wf,
itermVar_wf,
itermConstant_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
less_than_wf,
intformand_wf,
intformless_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_formula_prop_le_lemma
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalAxiom,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
lambdaFormation,
unionElimination,
equalityElimination,
because_Cache,
productElimination,
independent_isectElimination,
instantiate,
cumulativity,
intEquality,
dependent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
promote_hyp,
independent_pairFormation
Latex:
\mforall{}[n:\mBbbN{}]. (||upto(n)|| \msim{} n)
Date html generated:
2017_04_17-AM-07_56_50
Last ObjectModification:
2017_02_27-PM-04_28_18
Theory : list_1
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