Nuprl Lemma : multiply_functionality_wrt_assoced

a,a',b,b':ℤ.  ((a a')  (b b')  ((a b) (a' b')))


Proof




Definitions occuring in Statement :  assoced: b all: x:A. B[x] implies:  Q multiply: m int:
Definitions unfolded in proof :  assoced: b all: x:A. B[x] implies:  Q and: P ∧ Q cand: c∧ B member: t ∈ T uall: [x:A]. B[x] prop: divides: a exists: x:A. B[x] uimplies: supposing a sq_type: SQType(T) guard: {T} decidable: Dec(P) or: P ∨ Q not: ¬A satisfiable_int_formula: satisfiable_int_formula(fmla) false: False top: Top subtype_rel: A ⊆B
Lemmas referenced :  divides_wf istype-int subtype_base_sq int_subtype_base decidable__equal_int full-omega-unsat intformnot_wf intformeq_wf itermMultiply_wf itermVar_wf int_formula_prop_not_lemma istype-void int_formula_prop_eq_lemma int_term_value_mul_lemma int_term_value_var_lemma int_formula_prop_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep Error :lambdaFormation_alt,  sqequalHypSubstitution productElimination thin cut independent_pairFormation hypothesis Error :productIsType,  Error :universeIsType,  introduction extract_by_obid isectElimination hypothesisEquality Error :inhabitedIsType,  promote_hyp instantiate cumulativity intEquality independent_isectElimination dependent_functionElimination equalityTransitivity equalitySymmetry independent_functionElimination Error :dependent_pairFormation_alt,  multiplyEquality because_Cache unionElimination natural_numberEquality approximateComputation Error :lambdaEquality_alt,  int_eqEquality Error :isect_memberEquality_alt,  voidElimination Error :equalityIsType4,  applyEquality

Latex:
\mforall{}a,a',b,b':\mBbbZ{}.    ((a  \msim{}  a')  {}\mRightarrow{}  (b  \msim{}  b')  {}\mRightarrow{}  ((a  *  b)  \msim{}  (a'  *  b')))



Date html generated: 2019_06_20-PM-02_21_01
Last ObjectModification: 2018_10_03-AM-00_35_53

Theory : num_thy_1


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