Nuprl Lemma : assoced_transitivity
∀a,b,c:ℤ. ((a ~ b) ⇒ (b ~ c) ⇒ (a ~ c))
Proof
Definitions occuring in Statement :
assoced: a ~ b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
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,
guard: {T},
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
divides_transitivity,
divides_wf,
istype-int
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :lambdaFormation_alt,
sqequalHypSubstitution,
productElimination,
thin,
cut,
hypothesis,
introduction,
extract_by_obid,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
independent_pairFormation,
Error :productIsType,
Error :universeIsType,
isectElimination,
Error :inhabitedIsType
Latex:
\mforall{}a,b,c:\mBbbZ{}. ((a \msim{} b) {}\mRightarrow{} (b \msim{} c) {}\mRightarrow{} (a \msim{} c))
Date html generated:
2019_06_20-PM-02_20_59
Last ObjectModification:
2018_10_03-AM-00_35_50
Theory : num_thy_1
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