Nuprl Lemma : fdl-0-not-1
∀[X:Type]. (¬(0 = 1 ∈ Point(free-dl(X))))
Proof
Definitions occuring in Statement :
free-dl: free-dl(X),
lattice-0: 0,
lattice-1: 1,
lattice-point: Point(l),
uall: ∀[x:A]. B[x],
not: ¬A,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
fdl-is-1: fdl-is-1(x),
bl-exists: (∃x∈L.P[x])_b,
reduce: reduce(f;k;as),
list_ind: list_ind,
lattice-0: 0,
record-select: r.x,
free-dl: free-dl(X),
mk-bounded-distributive-lattice: mk-bounded-distributive-lattice,
mk-bounded-lattice: mk-bounded-lattice(T;m;j;z;o),
record-update: r[x := v],
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
bfalse: ff,
btrue: tt,
nil: [],
it: ⋅,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a
Lemmas referenced :
assert_of_ff,
fdl-eq-1,
equal_wf,
not_wf,
assert_wf,
fdl-is-1_wf,
lattice-0_wf,
free-dl_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,
lattice-meet_wf,
lattice-join_wf,
bdd-distributive-lattice_wf,
lattice-1_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
sqequalRule,
extract_by_obid,
hypothesis,
addLevel,
sqequalHypSubstitution,
impliesFunctionality,
isectElimination,
hypothesisEquality,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_functionElimination,
because_Cache,
cumulativity,
applyEquality,
voidElimination,
instantiate,
lambdaEquality,
productEquality,
universeEquality,
independent_isectElimination,
setElimination,
rename
Latex:
\mforall{}[X:Type]. (\mneg{}(0 = 1))
Date html generated:
2020_05_20-AM-08_42_50
Last ObjectModification:
2017_07_28-AM-09_13_41
Theory : lattices
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