Nuprl Lemma : id-is-dma-hom
∀[dma:DeMorganAlgebra]. (λx.x ∈ dma-hom(dma;dma))
Proof
Definitions occuring in Statement :
dma-hom: dma-hom(dma1;dma2),
DeMorgan-algebra: DeMorganAlgebra,
uall: ∀[x:A]. B[x],
member: t ∈ T,
lambda: λx.A[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
dma-hom: dma-hom(dma1;dma2),
DeMorgan-algebra: DeMorganAlgebra,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
guard: {T},
uimplies: b supposing a,
so_apply: x[s],
bounded-lattice-hom: Hom(l1;l2),
lattice-hom: Hom(l1;l2)
Lemmas referenced :
dma-neg_wf,
lattice-point_wf,
subtype_rel_set,
DeMorgan-algebra-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
DeMorgan-algebra-structure-subtype,
subtype_rel_transitivity,
bounded-lattice-structure_wf,
bounded-lattice-axioms_wf,
uall_wf,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
DeMorgan-algebra-axioms_wf,
DeMorgan-algebra_wf,
id-is-bounded-lattice-hom,
bdd-distributive-lattice-subtype-bdd-lattice,
DeMorgan-algebra-subtype,
bdd-distributive-lattice_wf,
bdd-lattice_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_set_memberEquality,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
applyEquality,
instantiate,
lambdaEquality,
productEquality,
independent_isectElimination,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[dma:DeMorganAlgebra]. (\mlambda{}x.x \mmember{} dma-hom(dma;dma))
Date html generated:
2020_05_20-AM-08_56_08
Last ObjectModification:
2015_12_28-PM-01_55_41
Theory : lattices
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