Nuprl Lemma : free-from-atom-nat
∀[a:Atom1]. ∀[n:ℕ]. a#n:ℕ
Proof
Definitions occuring in Statement :
nat: ℕ,
free-from-atom: a#x:T,
atom: Atom$n,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
true: True,
less_than': less_than'(a;b),
le: A ≤ B,
top: Top,
subtype_rel: A ⊆r B,
subtract: n - m,
uiff: uiff(P;Q),
rev_implies: P ⇐ Q,
not: ¬A,
and: P ∧ Q,
iff: P ⇐⇒ Q,
or: P ∨ Q,
decidable: Dec(P),
all: ∀x:A. B[x],
prop: ℙ,
uimplies: b supposing a,
guard: {T},
ge: i ≥ j ,
false: False,
implies: P ⇒ Q,
nat: ℕ,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
subtract-add-cancel,
not-le-2,
le_reflexive,
le_wf,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-one-mul-top,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
nat_wf
Rules used in proof :
atomnEquality,
because_Cache,
minusEquality,
intEquality,
voidEquality,
isect_memberEquality,
applyEquality,
addEquality,
productElimination,
independent_pairFormation,
unionElimination,
freeFromAtomAxiom,
dependent_functionElimination,
lambdaEquality,
sqequalRule,
voidElimination,
independent_functionElimination,
independent_isectElimination,
natural_numberEquality,
lambdaFormation,
intWeakElimination,
rename,
setElimination,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
lemma_by_obid,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
dependent_set_memberEquality,
freeFromAtomTriviality,
extract_by_obid,
freeFromAtomApplication
Latex:
\mforall{}[a:Atom1]. \mforall{}[n:\mBbbN{}]. a\#n:\mBbbN{}
Date html generated:
2019_06_20-PM-00_25_47
Last ObjectModification:
2018_08_15-PM-03_08_53
Theory : int_1
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