Nuprl Lemma : DeMorgan-algebra-axioms_wf
∀[dma:DeMorganAlgebraStructure]. (DeMorgan-algebra-axioms(dma) ∈ ℙ)
Proof
Definitions occuring in Statement :
DeMorgan-algebra-axioms: DeMorgan-algebra-axioms(dma),
DeMorgan-algebra-structure: DeMorganAlgebraStructure,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
DeMorgan-algebra-axioms: DeMorgan-algebra-axioms(dma),
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
all_wf,
lattice-point_wf,
bounded-lattice-structure-subtype,
DeMorgan-algebra-structure-subtype,
subtype_rel_transitivity,
DeMorgan-algebra-structure_wf,
bounded-lattice-structure_wf,
lattice-structure_wf,
equal_wf,
dma-neg_wf,
lattice-meet_wf,
lattice-join_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
productEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
instantiate,
independent_isectElimination,
lambdaEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[dma:DeMorganAlgebraStructure]. (DeMorgan-algebra-axioms(dma) \mmember{} \mBbbP{})
Date html generated:
2020_05_20-AM-08_55_22
Last ObjectModification:
2015_12_28-PM-01_56_00
Theory : lattices
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