Nuprl Lemma : ni-min_wf
∀[f,g:ℕ∞]. (ni-min(f;g) ∈ ℕ∞)
Proof
Definitions occuring in Statement :
ni-min: ni-min(f;g),
nat-inf: ℕ∞,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
nat-inf: ℕ∞,
uall: ∀[x:A]. B[x],
member: t ∈ T,
ni-min: ni-min(f;g),
all: ∀x:A. B[x],
implies: P ⇒ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
uimplies: b supposing a,
cand: A c∧ B,
nat: ℕ,
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,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
btrue: tt,
assert: ↑b,
true: True,
bfalse: ff,
bool: 𝔹,
unit: Unit,
it: ⋅,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T}
Lemmas referenced :
band_wf,
nat_wf,
assert_of_band,
bool_cases_sqequal,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
le_wf,
assert_wf,
bool_wf,
eqtt_to_assert,
equal_wf,
all_wf,
set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
setElimination,
thin,
rename,
sqequalRule,
dependent_set_memberEquality,
lambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
applyEquality,
functionExtensionality,
hypothesisEquality,
hypothesis,
lambdaFormation,
productElimination,
independent_isectElimination,
dependent_functionElimination,
because_Cache,
addEquality,
natural_numberEquality,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
functionEquality,
axiomEquality
Latex:
\mforall{}[f,g:\mBbbN{}\minfty{}]. (ni-min(f;g) \mmember{} \mBbbN{}\minfty{})
Date html generated:
2017_10_01-AM-08_30_00
Last ObjectModification:
2017_07_26-PM-04_24_17
Theory : basic
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