Nuprl Lemma : imin_add_r
∀[a,b,c:ℤ]. ((imin(a;b) + c) = imin(a + c;b + c) ∈ ℤ)
Proof
Definitions occuring in Statement :
imin: imin(a;b),
uall: ∀[x:A]. B[x],
add: n + m,
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,
top: Top,
true: True,
squash: ↓T,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
minus_mono_wrt_eq,
imin_wf,
minus-add,
minus-one-mul,
add-commutes,
imax_wf,
equal_wf,
imax_add_r,
iff_weakening_equal,
add_com,
squash_wf,
true_wf,
add_functionality_wrt_eq,
minus_imin
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
addEquality,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
intEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
voidElimination,
voidEquality,
multiplyEquality,
minusEquality,
natural_numberEquality,
applyEquality,
lambdaEquality,
imageElimination,
imageMemberEquality,
baseClosed,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
universeEquality
Latex:
\mforall{}[a,b,c:\mBbbZ{}]. ((imin(a;b) + c) = imin(a + c;b + c))
Date html generated:
2017_04_14-AM-09_14_42
Last ObjectModification:
2017_02_27-PM-03_51_55
Theory : int_2
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