Nuprl Lemma : ni-max-nat
∀[n,m:ℕ]. (ni-max(n∞;m∞) = imax(n;m)∞ ∈ ℕ∞)
Proof
Definitions occuring in Statement :
ni-max: ni-max(f;g)
,
nat2inf: n∞
,
nat-inf: ℕ∞
,
imax: imax(a;b)
,
nat: ℕ
,
uall: ∀[x:A]. B[x]
,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
nat-inf: ℕ∞
,
all: ∀x:A. B[x]
,
implies: P
⇒ Q
,
prop: ℙ
,
subtype_rel: A ⊆r B
,
nat: ℕ
,
ge: i ≥ j
,
decidable: Dec(P)
,
or: P ∨ Q
,
uimplies: b supposing a
,
satisfiable_int_formula: satisfiable_int_formula(fmla)
,
exists: ∃x:A. B[x]
,
false: False
,
not: ¬A
,
top: Top
,
and: P ∧ Q
,
so_lambda: λ2x.t[x]
,
so_apply: x[s]
,
nat2inf: n∞
,
ni-max: ni-max(f;g)
,
iff: P
⇐⇒ Q
,
rev_implies: P
⇐ Q
,
uiff: uiff(P;Q)
,
guard: {T}
Lemmas referenced :
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
imax_strict_ub,
assert_of_lt_int,
assert_of_bor,
iff_weakening_uiff,
iff_transitivity,
iff_wf,
less_than_wf,
or_wf,
imax_wf,
lt_int_wf,
bor_wf,
iff_imp_equal_bool,
nat_wf,
all_wf,
le_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
nat2inf_wf,
ni-max_wf,
assert_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_set_memberEquality,
lambdaFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesisEquality,
hypothesis,
because_Cache,
sqequalRule,
addEquality,
setElimination,
rename,
natural_numberEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
functionEquality,
axiomEquality,
functionExtensionality,
addLevel,
productElimination,
impliesFunctionality,
independent_functionElimination,
orFunctionality,
inlFormation,
inrFormation
Latex:
\mforall{}[n,m:\mBbbN{}]. (ni-max(n\minfty{};m\minfty{}) = imax(n;m)\minfty{})
Date html generated:
2016_05_15-PM-01_48_08
Last ObjectModification:
2016_01_15-PM-11_16_20
Theory : basic
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