Nuprl Lemma : free-dml-0-not-1
∀T:Type. ∀eq:EqDecider(T). (¬(0 = 1 ∈ Point(free-DeMorgan-lattice(T;eq))))
Proof
Definitions occuring in Statement :
free-DeMorgan-lattice: free-DeMorgan-lattice(T;eq),
lattice-0: 0,
lattice-1: 1,
lattice-point: Point(l),
deq: EqDecider(T),
all: ∀x:A. B[x],
not: ¬A,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
false: False,
free-DeMorgan-lattice: free-DeMorgan-lattice(T;eq),
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice,
so_lambda: λ2x.t[x],
and: P ∧ Q,
so_apply: x[s],
uimplies: b supposing a
Lemmas referenced :
free-dl-0-not-1,
union-deq_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-0_wf,
bdd-distributive-lattice_wf,
lattice-1_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
unionEquality,
hypothesisEquality,
isectElimination,
hypothesis,
independent_functionElimination,
voidElimination,
cumulativity,
applyEquality,
instantiate,
lambdaEquality,
productEquality,
universeEquality,
because_Cache,
independent_isectElimination,
setElimination,
rename
Latex:
\mforall{}T:Type. \mforall{}eq:EqDecider(T). (\mneg{}(0 = 1))
Date html generated:
2020_05_20-AM-08_53_52
Last ObjectModification:
2015_12_28-PM-01_57_04
Theory : lattices
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