Nuprl Lemma : imin_assoc
∀[a,b,c:ℤ]. (imin(a;imin(b;c)) = imin(imin(a;b);c) ∈ ℤ)
Proof
Definitions occuring in Statement :
imin: imin(a;b),
uall: ∀[x:A]. B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
minus_mono_wrt_eq,
imin_wf,
equal_wf,
squash_wf,
true_wf,
istype-universe,
minus_imin,
subtype_rel_self,
iff_weakening_equal,
imax_wf,
imax_assoc,
istype-int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
applyEquality,
Error :lambdaEquality_alt,
imageElimination,
equalityTransitivity,
equalitySymmetry,
Error :universeIsType,
Error :inhabitedIsType,
instantiate,
universeEquality,
intEquality,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
because_Cache,
independent_functionElimination,
minusEquality,
Error :isect_memberEquality_alt,
axiomEquality,
Error :isectIsTypeImplies
Latex:
\mforall{}[a,b,c:\mBbbZ{}]. (imin(a;imin(b;c)) = imin(imin(a;b);c))
Date html generated:
2019_06_20-PM-01_13_52
Last ObjectModification:
2019_01_17-AM-08_43_47
Theory : int_2
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