Nuprl Lemma : mul-nat
∀[x,y:ℕ]. (x * y ∈ ℕ)
Proof
Definitions occuring in Statement :
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
multiply: n * m
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
prop: ℙ
Lemmas referenced :
mul_bounds_1a,
le_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_set_memberEquality,
multiplyEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
hypothesisEquality,
lemma_by_obid,
isectElimination,
hypothesis,
natural_numberEquality,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[x,y:\mBbbN{}]. (x * y \mmember{} \mBbbN{})
Date html generated:
2016_05_14-AM-07_34_11
Last ObjectModification:
2015_12_26-PM-01_23_34
Theory : int_2
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