Nuprl Lemma : combinations_wf
∀[n,m:ℕ]. (C(n;m) ∈ ℕ)
Proof
Definitions occuring in Statement :
combinations: C(n;m),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
combinations: C(n;m),
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
combinations_aux_wf,
false_wf,
le_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[n,m:\mBbbN{}]. (C(n;m) \mmember{} \mBbbN{})
Date html generated:
2016_05_15-PM-05_58_32
Last ObjectModification:
2015_12_27-PM-00_22_16
Theory : general
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