Nuprl Lemma : divides_anti_sym
∀a,b:ℤ. ((a | b) ⇒ (b | a) ⇒ a = ± b)
Proof
Definitions occuring in Statement :
divides: b | a,
pm_equal: i = ± j,
all: ∀x:A. B[x],
implies: P ⇒ Q,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
uimplies: b supposing a
Lemmas referenced :
divides_wf,
istype-int,
divides_of_absvals,
absval_eq,
divides_anti_sym_n,
absval_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
Error :universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
Error :inhabitedIsType,
dependent_functionElimination,
productElimination,
independent_pairFormation,
independent_functionElimination,
independent_isectElimination
Latex:
\mforall{}a,b:\mBbbZ{}. ((a | b) {}\mRightarrow{} (b | a) {}\mRightarrow{} a = \mpm{} b)
Date html generated:
2019_06_20-PM-02_20_12
Last ObjectModification:
2018_10_03-AM-00_35_45
Theory : num_thy_1
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