Nuprl Lemma : stamps-example-ext
∀n:ℕ. ∃i:ℕ. (∃j:ℕ [((n + 8) = ((3 * i) + (5 * j)) ∈ ℤ)])
Proof
Definitions occuring in Statement :
nat: ℕ,
all: ∀x:A. B[x],
sq_exists: ∃x:A [B[x]],
exists: ∃x:A. B[x],
multiply: n * m,
add: n + m,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
stamps-example,
decidable__le,
decidable__and,
uall: ∀[x:A]. B[x],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
uimplies: b supposing a,
strict4: strict4(F),
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
prop: ℙ,
guard: {T},
or: P ∨ Q,
squash: ↓T,
decidable__not,
decidable__implies,
decidable__less_than',
decidable__false,
subtract: n - m
Lemmas referenced :
stamps-example,
lifting-strict-decide,
top_wf,
equal_wf,
has-value_wf_base,
base_wf,
is-exception_wf,
lifting-strict-less,
decidable__le,
decidable__and,
decidable__not,
decidable__implies,
decidable__less_than',
decidable__false
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
isectElimination,
baseClosed,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
callbyvalueDecide,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
unionEquality,
unionElimination,
sqleReflexivity,
dependent_functionElimination,
independent_functionElimination,
baseApply,
closedConclusion,
decideExceptionCases,
inrFormation,
because_Cache,
imageMemberEquality,
imageElimination,
exceptionSqequal,
inlFormation
Latex:
\mforall{}n:\mBbbN{}. \mexists{}i:\mBbbN{}. (\mexists{}j:\mBbbN{} [((n + 8) = ((3 * i) + (5 * j)))])
Date html generated:
2019_06_20-PM-01_05_04
Last ObjectModification:
2019_06_20-PM-01_00_03
Theory : int_1
Home
Index