Nuprl Lemma : assert-is-dml-1
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[x:Point(free-DeMorgan-lattice(T;eq))].
uiff(↑is-dml-1(T;eq;x);x = 1 ∈ Point(free-DeMorgan-lattice(T;eq)))
Proof
Definitions occuring in Statement :
is-dml-1: is-dml-1(T;eq;x),
free-DeMorgan-lattice: free-DeMorgan-lattice(T;eq),
lattice-1: 1,
lattice-point: Point(l),
deq: EqDecider(T),
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
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,
uiff: uiff(P;Q),
implies: P ⇒ Q,
is-dml-1: is-dml-1(T;eq;x),
all: ∀x:A. B[x],
deq: EqDecider(T),
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
assert_wf,
is-dml-1_wf,
equal_wf,
lattice-point_wf,
free-DeMorgan-lattice_wf,
subtype_rel_set,
bounded-lattice-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
bounded-lattice-axioms_wf,
uall_wf,
lattice-meet_wf,
lattice-join_wf,
lattice-1_wf,
bdd-distributive-lattice_wf,
deq_wf,
assert_witness,
free-dml-deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
applyEquality,
sqequalRule,
instantiate,
lambdaEquality,
productEquality,
universeEquality,
because_Cache,
independent_isectElimination,
setElimination,
rename,
isect_memberFormation,
productElimination,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
lambdaFormation,
dependent_functionElimination,
independent_pairFormation,
functionExtensionality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[x:Point(free-DeMorgan-lattice(T;eq))].
uiff(\muparrow{}is-dml-1(T;eq;x);x = 1)
Date html generated:
2020_05_20-AM-08_54_03
Last ObjectModification:
2017_07_28-AM-09_16_38
Theory : lattices
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