Nuprl Lemma : ndiff_add_eq_imax
∀[a,b:ℤ]. (((a -- b) + b) = imax(a;b) ∈ ℤ)
Proof
Definitions occuring in Statement :
ndiff: a -- b,
imax: imax(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,
ndiff: a -- b,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
subtract: n - m,
top: Top
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
imax_add_r,
subtract_wf,
imax_wf,
iff_weakening_equal,
add-associates,
minus-one-mul,
add-commutes,
minus-one-mul-top,
add-mul-special,
zero-mul,
add-zero,
zero-add
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
intEquality,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
axiomEquality,
because_Cache,
applyEquality,
lambdaEquality,
imageElimination,
extract_by_obid,
equalityTransitivity,
equalitySymmetry,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination,
voidElimination,
voidEquality,
minusEquality
Latex:
\mforall{}[a,b:\mBbbZ{}]. (((a -- b) + b) = imax(a;b))
Date html generated:
2017_04_14-AM-09_15_03
Last ObjectModification:
2017_02_27-PM-03_52_43
Theory : int_2
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