Nuprl Lemma : lattice-equiv_wf
∀[l:GeneralBoundedLatticeStructure]. ∀[a,b:Point(l)]. (a ≡ b ∈ ℙ)
Proof
Definitions occuring in Statement :
lattice-equiv: a ≡ b,
general-bounded-lattice-structure: GeneralBoundedLatticeStructure,
lattice-point: Point(l),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
lattice-equiv: a ≡ b,
general-bounded-lattice-structure: GeneralBoundedLatticeStructure,
record+: record+,
record-select: r.x,
subtype_rel: A ⊆r B,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
guard: {T},
prop: ℙ,
lattice-point: Point(l),
uimplies: b supposing a
Lemmas referenced :
subtype_rel_self,
lattice-point_wf,
bounded-lattice-structure-subtype,
general-bounded-lattice-structure-subtype,
subtype_rel_transitivity,
general-bounded-lattice-structure_wf,
bounded-lattice-structure_wf,
lattice-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
dependentIntersectionElimination,
dependentIntersectionEqElimination,
thin,
hypothesis,
applyEquality,
tokenEquality,
instantiate,
lemma_by_obid,
isectElimination,
universeEquality,
functionEquality,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
cumulativity,
hypothesisEquality,
because_Cache,
axiomEquality,
independent_isectElimination,
isect_memberEquality
Latex:
\mforall{}[l:GeneralBoundedLatticeStructure]. \mforall{}[a,b:Point(l)]. (a \mequiv{} b \mmember{} \mBbbP{})
Date html generated:
2020_05_20-AM-08_57_57
Last ObjectModification:
2015_12_28-PM-01_54_48
Theory : lattices
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