Nuprl Lemma : assoced_elim
∀a,b:ℤ. (a ~ b ⇐⇒ (a = b ∈ ℤ) ∨ (a = (-b) ∈ ℤ))
Proof
Definitions occuring in Statement :
assoced: a ~ b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
minus: -n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
assoced: a ~ b,
member: t ∈ T,
pm_equal: i = ± j,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
or: P ∨ Q,
subtype_rel: A ⊆r B,
rev_implies: P ⇐ Q,
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
istype-int,
int_subtype_base,
assoc_reln,
divides_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
Error :inhabitedIsType,
hypothesisEquality,
cut,
introduction,
extract_by_obid,
hypothesis,
independent_pairFormation,
sqequalRule,
Error :unionIsType,
Error :equalityIsType4,
applyEquality,
sqequalHypSubstitution,
because_Cache,
minusEquality,
productElimination,
thin,
independent_functionElimination,
dependent_functionElimination,
Error :productIsType,
Error :universeIsType,
isectElimination,
promote_hyp
Latex:
\mforall{}a,b:\mBbbZ{}. (a \msim{} b \mLeftarrow{}{}\mRightarrow{} (a = b) \mvee{} (a = (-b)))
Date html generated:
2019_06_20-PM-02_21_06
Last ObjectModification:
2018_10_03-AM-10_23_38
Theory : num_thy_1
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