Nuprl Lemma : DeMorgan-algebra_wf
DeMorganAlgebra ∈ 𝕌'
Proof
Definitions occuring in Statement :
DeMorgan-algebra: DeMorganAlgebra,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
DeMorgan-algebra: DeMorganAlgebra,
member: t ∈ T,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
DeMorgan-algebra-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
DeMorgan-algebra-structure-subtype,
subtype_rel_transitivity,
bounded-lattice-structure_wf,
lattice-structure_wf,
bounded-lattice-axioms_wf,
uall_wf,
lattice-point_wf,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
DeMorgan-algebra-axioms_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
setEquality,
cut,
lemma_by_obid,
hypothesis,
productEquality,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
instantiate,
independent_isectElimination,
lambdaEquality,
cumulativity,
universeEquality,
because_Cache
Latex:
DeMorganAlgebra \mmember{} \mBbbU{}'
Date html generated:
2020_05_20-AM-08_55_29
Last ObjectModification:
2015_12_28-PM-01_55_57
Theory : lattices
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