Nuprl Lemma : lattice-ble_wf
∀[l:LatticeStructure]. ∀[eq:EqDecider(Point(l))]. ∀[a,b:Point(l)]. (lattice-ble(l;eq;a;b) ∈ 𝔹)
Proof
Definitions occuring in Statement :
lattice-ble: lattice-ble(l;eq;a;b),
lattice-point: Point(l),
lattice-structure: LatticeStructure,
deq: EqDecider(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
lattice-ble: lattice-ble(l;eq;a;b),
deq: EqDecider(T)
Lemmas referenced :
lattice-meet_wf,
lattice-point_wf,
deq_wf,
lattice-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
applyEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
hypothesisEquality,
lemma_by_obid,
isectElimination,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[l:LatticeStructure]. \mforall{}[eq:EqDecider(Point(l))]. \mforall{}[a,b:Point(l)]. (lattice-ble(l;eq;a;b) \mmember{} \mBbbB{})
Date html generated:
2020_05_20-AM-08_43_06
Last ObjectModification:
2015_12_28-PM-02_01_45
Theory : lattices
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