Nuprl Lemma : DeMorgan-algebra-subtype
DeMorganAlgebra ⊆r BoundedDistributiveLattice
Proof
Definitions occuring in Statement :
DeMorgan-algebra: DeMorganAlgebra,
bdd-distributive-lattice: BoundedDistributiveLattice,
subtype_rel: A ⊆r B
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
member: t ∈ T,
DeMorgan-algebra: DeMorganAlgebra,
bdd-distributive-lattice: BoundedDistributiveLattice,
and: P ∧ Q,
cand: A c∧ B,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
DeMorgan-algebra-structure-subtype,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
bounded-lattice-axioms_wf,
uall_wf,
lattice-point_wf,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
DeMorgan-algebra_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,
productEquality,
isectElimination,
because_Cache
Latex:
DeMorganAlgebra \msubseteq{}r BoundedDistributiveLattice
Date html generated:
2020_05_20-AM-08_55_33
Last ObjectModification:
2015_12_28-PM-01_55_53
Theory : lattices
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