Nuprl Lemma : bdd-distributive-lattice-subtype-distributive-lattice
BoundedDistributiveLattice ⊆r DistributiveLattice
Proof
Definitions occuring in Statement :
bdd-distributive-lattice: BoundedDistributiveLattice,
distributive-lattice: DistributiveLattice,
subtype_rel: A ⊆r B
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
member: t ∈ T,
bdd-distributive-lattice: BoundedDistributiveLattice,
distributive-lattice: DistributiveLattice,
and: P ∧ Q,
cand: A c∧ B,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ
Lemmas referenced :
bounded-lattice-structure-subtype,
and_wf,
lattice-axioms_wf,
uall_wf,
lattice-point_wf,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
bdd-distributive-lattice_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
cut,
dependent_set_memberEquality,
hypothesisEquality,
applyEquality,
lemma_by_obid,
hypothesis,
sqequalRule,
productElimination,
independent_pairFormation,
isectElimination
Latex:
BoundedDistributiveLattice \msubseteq{}r DistributiveLattice
Date html generated:
2020_05_20-AM-08_25_10
Last ObjectModification:
2015_12_28-PM-02_03_16
Theory : lattices
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