Nuprl Lemma : mul-non-neg1
∀[x,y:ℤ]. (0 ≤ (x * y)) supposing ((0 ≤ y) and (0 ≤ x))
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
multiply: n * m,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
nat: ℕ,
prop: ℙ,
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
false: False
Lemmas referenced :
mul_bounds_1a,
le_wf,
less_than'_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_set_memberEquality,
hypothesisEquality,
hypothesis,
natural_numberEquality,
because_Cache,
sqequalRule,
productElimination,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
multiplyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
intEquality,
voidElimination
Latex:
\mforall{}[x,y:\mBbbZ{}]. (0 \mleq{} (x * y)) supposing ((0 \mleq{} y) and (0 \mleq{} x))
Date html generated:
2016_05_14-AM-07_20_45
Last ObjectModification:
2015_12_26-PM-01_32_01
Theory : int_2
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