Nuprl Lemma : lcm-unique
∀n,m,l:ℕ+. ((((n | l) ∧ (m | l)) ∧ (∀v:ℤ. ((n | v) ⇒ (m | v) ⇒ (l | v)))) ⇒ (l = lcm(n;m) ∈ ℤ))
Proof
Definitions occuring in Statement :
lcm: lcm(a;b),
divides: b | a,
nat_plus: ℕ+,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
member: t ∈ T,
subtype_rel: A ⊆r B,
nat: ℕ,
uall: ∀[x:A]. B[x],
nat_plus: ℕ+,
uimplies: b supposing a,
prop: ℙ,
iff: P ⇐⇒ Q,
assoced: a ~ b,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T}
Lemmas referenced :
lcm-is-lcm,
assoced_nelim,
nat_plus_subtype_nat,
lcm_wf,
le_weakening2,
lcm-positive,
le_wf,
and_wf,
divides_wf,
all_wf,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalHypSubstitution,
productElimination,
thin,
lemma_by_obid,
dependent_functionElimination,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
dependent_set_memberEquality,
isectElimination,
setElimination,
rename,
natural_numberEquality,
independent_isectElimination,
independent_functionElimination,
independent_pairFormation,
intEquality,
lambdaEquality,
functionEquality
Latex:
\mforall{}n,m,l:\mBbbN{}\msupplus{}. ((((n | l) \mwedge{} (m | l)) \mwedge{} (\mforall{}v:\mBbbZ{}. ((n | v) {}\mRightarrow{} (m | v) {}\mRightarrow{} (l | v)))) {}\mRightarrow{} (l = lcm(n;m)))
Date html generated:
2016_05_14-PM-09_25_11
Last ObjectModification:
2015_12_26-PM-08_03_07
Theory : num_thy_1
Home
Index