Nuprl Lemma : is-dml-1_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[x:Point(free-DeMorgan-lattice(T;eq))]. (is-dml-1(T;eq;x) ∈ 𝔹)
Proof
Definitions occuring in Statement :
is-dml-1: is-dml-1(T;eq;x),
free-DeMorgan-lattice: free-DeMorgan-lattice(T;eq),
lattice-point: Point(l),
deq: EqDecider(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
is-dml-1: is-dml-1(T;eq;x),
subtype_rel: A ⊆r B,
deq: EqDecider(T),
bdd-distributive-lattice: BoundedDistributiveLattice,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
uimplies: b supposing a
Lemmas referenced :
free-dml-deq_wf,
deq_wf,
lattice-1_wf,
free-DeMorgan-lattice_wf,
bdd-distributive-lattice_wf,
lattice-point_wf,
subtype_rel_set,
bounded-lattice-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
bounded-lattice-axioms_wf,
uall_wf,
equal_wf,
lattice-meet_wf,
lattice-join_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
applyEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
setElimination,
rename,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
instantiate,
productEquality,
universeEquality,
independent_isectElimination,
isect_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[x:Point(free-DeMorgan-lattice(T;eq))]. (is-dml-1(T;eq;x) \mmember{} \mBbbB{})
Date html generated:
2020_05_20-AM-08_53_59
Last ObjectModification:
2015_12_28-PM-01_56_48
Theory : lattices
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