Nuprl Lemma : dma-hom_wf
∀[dma1:DeMorganAlgebra]. ∀dma2:DeMorganAlgebra. (dma-hom(dma1;dma2) ∈ Type)
Proof
Definitions occuring in Statement :
dma-hom: dma-hom(dma1;dma2),
DeMorgan-algebra: DeMorganAlgebra,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
dma-hom: dma-hom(dma1;dma2),
subtype_rel: A ⊆r B,
DeMorgan-algebra: DeMorganAlgebra,
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 :
bounded-lattice-hom_wf,
subtype_rel_set,
DeMorgan-algebra-structure_wf,
bounded-lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
DeMorgan-algebra-structure-subtype,
subtype_rel_transitivity,
lattice-structure_wf,
bounded-lattice-axioms_wf,
uall_wf,
lattice-point_wf,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
DeMorgan-algebra-axioms_wf,
dma-neg_wf,
DeMorgan-algebra_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalRule,
setEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
instantiate,
hypothesis,
lambdaEquality,
productEquality,
independent_isectElimination,
cumulativity,
universeEquality,
because_Cache,
setElimination,
rename,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[dma1:DeMorganAlgebra]. \mforall{}dma2:DeMorganAlgebra. (dma-hom(dma1;dma2) \mmember{} Type)
Date html generated:
2020_05_20-AM-08_56_04
Last ObjectModification:
2015_12_28-PM-01_55_37
Theory : lattices
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