Nuprl Lemma : gcd_p_sym

a,b,y:ℤ.  (GCD(a;b;y)  GCD(b;a;y))


Proof




Definitions occuring in Statement :  gcd_p: GCD(a;b;y) all: x:A. B[x] implies:  Q int:
Definitions unfolded in proof :  gcd_p: GCD(a;b;y) all: x:A. B[x] implies:  Q and: P ∧ Q cand: c∧ B member: t ∈ T uall: [x:A]. B[x] prop:
Lemmas referenced :  divides_wf istype-int
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep Error :lambdaFormation_alt,  sqequalHypSubstitution productElimination thin cut hypothesis independent_pairFormation dependent_functionElimination hypothesisEquality independent_functionElimination Error :productIsType,  Error :universeIsType,  introduction extract_by_obid isectElimination Error :inhabitedIsType,  Error :functionIsType

Latex:
\mforall{}a,b,y:\mBbbZ{}.    (GCD(a;b;y)  {}\mRightarrow{}  GCD(b;a;y))



Date html generated: 2019_06_20-PM-02_21_35
Last ObjectModification: 2018_10_02-PM-11_35_09

Theory : num_thy_1


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