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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