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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