Nuprl Lemma : loset_connex
∀s:LOSet. ∀x,y:|s|. ((x ≤ y) ∨ (y ≤ x))
Proof
Definitions occuring in Statement :
loset: LOSet,
set_leq: a ≤ b,
set_car: |p|,
all: ∀x:A. B[x],
or: P ∨ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
connex: Connex(T;x,y.R[x; y])
Lemmas referenced :
loset_properties,
loset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis
Latex:
\mforall{}s:LOSet. \mforall{}x,y:|s|. ((x \mleq{} y) \mvee{} (y \mleq{} x))
Date html generated:
2016_05_15-PM-00_05_27
Last ObjectModification:
2015_12_26-PM-11_27_40
Theory : sets_1
Home
Index