### Nuprl Lemma : multiply-is-int-iff

`∀[a,b:Base].  uiff(a * b ∈ ℤ;(a ∈ ℤ) ∧ (b ∈ ℤ))`

Proof

Definitions occuring in Statement :  uiff: `uiff(P;Q)` uall: `∀[x:A]. B[x]` and: `P ∧ Q` member: `t ∈ T` multiply: `n * m` int: `ℤ` base: `Base`
Definitions unfolded in proof :  prop: `ℙ` uimplies: `b supposing a` and: `P ∧ Q` uiff: `uiff(P;Q)` member: `t ∈ T` uall: `∀[x:A]. B[x]`
Lemmas referenced :  equal-wf-base base_wf
Rules used in proof :  isect_memberEquality productEquality because_Cache hypothesisEquality baseClosed closedConclusion baseApply intEquality isectElimination lemma_by_obid equalitySymmetry hypothesis equalityTransitivity axiomEquality independent_pairEquality thin productElimination sqequalHypSubstitution sqequalRule independent_pairFormation cut introduction isect_memberFormation sqequalReflexivity computationStep sqequalTransitivity sqequalSubstitution callbyvalueMultiply callbyvalueInt multiplyEquality

Latex:
\mforall{}[a,b:Base].    uiff(a  *  b  \mmember{}  \mBbbZ{};(a  \mmember{}  \mBbbZ{})  \mwedge{}  (b  \mmember{}  \mBbbZ{}))

Date html generated: 2019_06_20-AM-11_21_56
Last ObjectModification: 2018_10_15-PM-03_40_02

Theory : arithmetic

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