Nuprl Lemma : mul_cancel_in_assoced
∀a,b:ℤ. ∀n:ℤ-o. (((n * a) ~ (n * b)) ⇒ (a ~ b))
Proof
Definitions occuring in Statement :
assoced: a ~ b,
int_nzero: ℤ-o,
all: ∀x:A. B[x],
implies: P ⇒ Q,
multiply: n * m,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
int_nzero: ℤ-o,
uall: ∀[x:A]. B[x],
prop: ℙ,
or: P ∨ Q,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
nequal: a ≠ b ∈ T ,
decidable: Dec(P),
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top
Lemmas referenced :
assoced_elim,
assoced_wf,
int_nzero_wf,
istype-int,
mul_cancel_in_eq,
int_subtype_base,
int_nzero_properties,
decidable__equal_int,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermMultiply_wf,
itermVar_wf,
itermMinus_wf,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_mul_lemma,
int_term_value_var_lemma,
int_term_value_minus_lemma,
int_formula_prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_functionElimination,
multiplyEquality,
setElimination,
rename,
because_Cache,
Error :universeIsType,
isectElimination,
Error :inhabitedIsType,
unionElimination,
Error :inlFormation_alt,
independent_isectElimination,
Error :equalityIsType4,
equalityTransitivity,
equalitySymmetry,
applyEquality,
sqequalRule,
minusEquality,
Error :inrFormation_alt,
natural_numberEquality,
approximateComputation,
Error :dependent_pairFormation_alt,
Error :lambdaEquality_alt,
int_eqEquality,
Error :isect_memberEquality_alt,
voidElimination,
independent_pairFormation
Latex:
\mforall{}a,b:\mBbbZ{}. \mforall{}n:\mBbbZ{}\msupminus{}\msupzero{}. (((n * a) \msim{} (n * b)) {}\mRightarrow{} (a \msim{} b))
Date html generated:
2019_06_20-PM-02_21_08
Last ObjectModification:
2018_10_03-AM-10_23_39
Theory : num_thy_1
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