Nuprl Lemma : free-dl-0-not-1
∀T:Type. ∀eq:EqDecider(T). (¬(0 = 1 ∈ Point(free-dist-lattice(T; eq))))
Proof
Definitions occuring in Statement :
free-dist-lattice: free-dist-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,
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
squash: ↓T,
free-dist-lattice: free-dist-lattice(T; eq),
lattice-1: 1,
lattice-0: 0,
mk-bounded-distributive-lattice: mk-bounded-distributive-lattice,
mk-bounded-lattice: mk-bounded-lattice(T;m;j;z;o),
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
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,
uiff: uiff(P;Q)
Lemmas referenced :
free-dl-point,
rec_select_update_lemma,
equal_wf,
lattice-point_wf,
free-dist-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,
member-fset-singleton,
fset_wf,
deq-fset_wf,
empty-fset_wf,
fset-member_wf,
mem_empty_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
sqequalHypSubstitution,
sqequalRule,
introduction,
extract_by_obid,
isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
imageMemberEquality,
hypothesisEquality,
baseClosed,
equalityUniverse,
levelHypothesis,
because_Cache,
imageElimination,
dependent_functionElimination,
independent_functionElimination,
cumulativity,
instantiate,
productEquality,
universeEquality,
independent_isectElimination,
productElimination,
equalitySymmetry,
hyp_replacement,
Error :applyLambdaEquality
Latex:
\mforall{}T:Type. \mforall{}eq:EqDecider(T). (\mneg{}(0 = 1))
Date html generated:
2016_10_26-PM-00_57_09
Last ObjectModification:
2016_07_12-AM-08_58_32
Theory : lattices
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