Nuprl Lemma : divides_preorder
Preorder(ℤ;x,y.x | y)
Proof
Definitions occuring in Statement :
divides: b | a,
preorder: Preorder(T;x,y.R[x; y]),
int: ℤ
Definitions unfolded in proof :
preorder: Preorder(T;x,y.R[x; y]),
trans: Trans(T;x,y.E[x; y]),
refl: Refl(T;x,y.E[x; y]),
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
member: t ∈ T,
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
divides_reflexivity,
istype-int,
divides_wf,
divides_transitivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
Error :lambdaFormation_alt,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
independent_pairFormation,
Error :universeIsType,
isectElimination,
Error :inhabitedIsType,
independent_functionElimination
Latex:
Preorder(\mBbbZ{};x,y.x | y)
Date html generated:
2019_06_20-PM-02_20_08
Last ObjectModification:
2018_10_03-AM-00_35_39
Theory : num_thy_1
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