Nuprl Lemma : free-from-atom-int
∀[a:Atom1]. ∀[n:ℤ]. a#n:ℤ
Proof
Definitions occuring in Statement :
free-from-atom: a#x:T,
atom: Atom$n,
uall: ∀[x:A]. B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
nat: ℕ,
uimplies: b supposing a,
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
subtype_rel: A ⊆r B,
top: Top,
subtract: n - m,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
true: True,
gt: i > j
Lemmas referenced :
not-gt-2,
free-from-atom-subtype,
less_than_wf,
omega-shadow,
add-swap,
add-associates,
false_wf,
less-iff-le,
zero-mul,
add-mul-special,
add-commutes,
zero-add,
one-mul,
add-zero,
minus-zero,
minus-one-mul-top,
le_reflexive,
subtract_wf,
add_functionality_wrt_le,
not-lt-2,
le_wf,
minus-one-mul,
le_weakening2,
free-from-atom-nat,
nat_wf,
minus-minus,
decidable__lt
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
natural_numberEquality,
hypothesis,
unionElimination,
freeFromAtomAxiom,
intEquality,
sqequalRule,
isect_memberEquality,
isectElimination,
because_Cache,
atomnEquality,
freeFromAtomApplication,
freeFromAtomTriviality,
lambdaEquality,
minusEquality,
setElimination,
rename,
dependent_set_memberEquality,
independent_isectElimination,
productElimination,
multiplyEquality,
applyEquality,
voidElimination,
voidEquality,
addEquality,
independent_pairFormation,
lambdaFormation,
imageMemberEquality,
baseClosed,
independent_functionElimination
Latex:
\mforall{}[a:Atom1]. \mforall{}[n:\mBbbZ{}]. a\#n:\mBbbZ{}
Date html generated:
2016_05_13-PM-04_03_55
Last ObjectModification:
2016_01_14-PM-07_24_26
Theory : int_1
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