Nuprl Lemma : stamps35_wf
∀n:ℕ. (stamps35(n) ∈ ∃i:ℕ. (∃j:ℕ [((n + 8) = ((3 * i) + (5 * j)) ∈ ℤ)]))
Proof
Definitions occuring in Statement :
stamps35: stamps35(n),
nat: ℕ,
all: ∀x:A. B[x],
sq_exists: ∃x:A [B[x]],
exists: ∃x:A. B[x],
member: t ∈ T,
multiply: n * m,
add: n + m,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
stamps35: stamps35(n),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
nat: ℕ,
so_apply: x[s],
sq_exists: ∃x:A [B[x]],
exists: ∃x:A. B[x],
prop: ℙ
Lemmas referenced :
stamps-example-ext,
subtype_rel_self,
nat_wf,
exists_wf,
sq_exists_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
applyEquality,
thin,
instantiate,
extract_by_obid,
hypothesis,
introduction,
sqequalHypSubstitution,
isectElimination,
functionEquality,
lambdaEquality,
intEquality,
addEquality,
setElimination,
rename,
hypothesisEquality,
natural_numberEquality,
multiplyEquality
Latex:
\mforall{}n:\mBbbN{}. (stamps35(n) \mmember{} \mexists{}i:\mBbbN{}. (\mexists{}j:\mBbbN{} [((n + 8) = ((3 * i) + (5 * j)))]))
Date html generated:
2018_05_21-PM-00_04_07
Last ObjectModification:
2018_05_19-AM-07_10_48
Theory : int_1
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