Nuprl Lemma : nim-sum-0
∀[x:ℕ]. (nim-sum(x;0) = x ∈ ℤ)
Proof
Definitions occuring in Statement :
nim-sum: nim-sum(x;y),
nat: ℕ,
uall: ∀[x:A]. B[x],
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
squash: ↓T,
prop: ℙ,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
nim-sum-com,
false_wf,
le_wf,
subtype_rel_self,
iff_weakening_equal,
nim_sum0_lemma,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeEquality,
intEquality,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
lambdaFormation,
setElimination,
rename,
imageMemberEquality,
baseClosed,
instantiate,
because_Cache,
independent_isectElimination,
productElimination,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[x:\mBbbN{}]. (nim-sum(x;0) = x)
Date html generated:
2018_05_21-PM-09_10_41
Last ObjectModification:
2018_05_19-PM-05_12_40
Theory : general
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