Nuprl Lemma : free-DeMorgan-algebra_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. (free-DeMorgan-algebra(T;eq) ∈ DeMorganAlgebra)
Proof
Definitions occuring in Statement :
free-DeMorgan-algebra: free-DeMorgan-algebra(T;eq),
DeMorgan-algebra: DeMorganAlgebra,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
free-DeMorgan-algebra: free-DeMorgan-algebra(T;eq),
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
uimplies: b supposing a,
cand: A c∧ B,
all: ∀x:A. B[x],
squash: ↓T,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
or: P ∨ Q
Lemmas referenced :
mk-DeMorgan-algebra_wf,
free-DeMorgan-lattice_wf,
dm-neg_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,
squash_wf,
true_wf,
dm-neg-neg,
iff_weakening_equal,
dm-neg-properties,
all_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
lambdaEquality,
because_Cache,
applyEquality,
instantiate,
productEquality,
universeEquality,
independent_isectElimination,
lambdaFormation,
imageElimination,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
independent_pairFormation,
inlFormation,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. (free-DeMorgan-algebra(T;eq) \mmember{} DeMorganAlgebra)
Date html generated:
2020_05_20-AM-08_56_20
Last ObjectModification:
2017_07_28-AM-09_17_21
Theory : lattices
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