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: a ~ b
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
multiply: n * m
, 
int: ℤ
Definitions unfolded in proof : 
assoced: a ~ b
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
and: P ∧ Q
, 
cand: A c∧ B
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
divides: b | a
, 
exists: ∃x:A. B[x]
, 
uimplies: b 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 ⊆r 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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