Nuprl Lemma : ni-min-assoc
∀[x,y,z:ℕ∞].  (ni-min(ni-min(x;y);z) = ni-min(x;ni-min(y;z)) ∈ ℕ∞)
Proof
Definitions occuring in Statement : 
ni-min: ni-min(f;g)
, 
nat-inf: 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∞
, 
squash: ↓T
, 
so_lambda: λ2x.t[x]
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
nat: ℕ
, 
ge: i ≥ j 
, 
all: ∀x:A. B[x]
, 
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_apply: x[s]
, 
ni-min: ni-min(f;g)
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
uiff: uiff(P;Q)
, 
band: p ∧b q
, 
ifthenelse: if b then t else f fi 
, 
bfalse: ff
, 
sq_type: SQType(T)
, 
guard: {T}
, 
bnot: ¬bb
, 
assert: ↑b
Lemmas referenced : 
ni-min_wf, 
all_wf, 
nat_wf, 
assert_wf, 
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, 
bool_wf, 
eqtt_to_assert, 
equal_wf, 
eqff_to_assert, 
bool_cases_sqequal, 
subtype_base_sq, 
bool_subtype_base, 
assert-bnot, 
bfalse_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
applyLambdaEquality, 
setElimination, 
rename, 
sqequalRule, 
imageMemberEquality, 
baseClosed, 
imageElimination, 
dependent_set_memberEquality, 
lambdaEquality, 
functionEquality, 
applyEquality, 
functionExtensionality, 
addEquality, 
natural_numberEquality, 
dependent_functionElimination, 
unionElimination, 
independent_isectElimination, 
dependent_pairFormation, 
int_eqEquality, 
intEquality, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
independent_pairFormation, 
computeAll, 
because_Cache, 
axiomEquality, 
lambdaFormation, 
equalityElimination, 
equalityTransitivity, 
equalitySymmetry, 
productElimination, 
independent_functionElimination, 
promote_hyp, 
instantiate, 
cumulativity
Latex:
\mforall{}[x,y,z:\mBbbN{}\minfty{}].    (ni-min(ni-min(x;y);z)  =  ni-min(x;ni-min(y;z)))
Date html generated:
2017_10_01-AM-08_30_07
Last ObjectModification:
2017_07_26-PM-04_24_22
Theory : basic
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