Nuprl Lemma : free-from-atom2-nat
∀[a:Atom2]. ∀[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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
not: ¬A,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
subtract: n - m,
subtype_rel: A ⊆r B,
top: Top,
le: A ≤ B,
less_than': less_than'(a;b),
true: True
Lemmas referenced :
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,
le_reflexive,
le_wf,
subtract-add-cancel,
not-le-2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
independent_functionElimination,
voidElimination,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
freeFromAtomAxiom,
unionElimination,
independent_pairFormation,
productElimination,
addEquality,
applyEquality,
isect_memberEquality,
voidEquality,
intEquality,
minusEquality,
because_Cache,
atomnEquality,
freeFromAtomTriviality,
dependent_set_memberEquality,
freeFromAtomApplication
Latex:
\mforall{}[a:Atom2]. \mforall{}[n:\mBbbN{}]. a\#n:\mBbbN{}
Date html generated:
2019_06_20-PM-00_25_49
Last ObjectModification:
2018_08_15-PM-03_09_30
Theory : int_1
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