Nuprl Lemma : lattice-axioms_wf
∀[l:LatticeStructure]. (lattice-axioms(l) ∈ ℙ)
Proof
Definitions occuring in Statement :
lattice-axioms: lattice-axioms(l)
,
lattice-structure: LatticeStructure
,
uall: ∀[x:A]. B[x]
,
prop: ℙ
,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
lattice-axioms: lattice-axioms(l)
,
prop: ℙ
,
and: P ∧ Q
,
so_lambda: λ2x.t[x]
,
so_apply: x[s]
Lemmas referenced :
uall_wf,
lattice-point_wf,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
lattice-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
productEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[l:LatticeStructure]. (lattice-axioms(l) \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-11_19_27
Last ObjectModification:
2015_12_28-PM-02_03_54
Theory : lattices
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