Nuprl Lemma : dM_inc_not_1
∀[I:fset(ℕ)]. ∀[x:names(I)]. (¬(<x> = 1 ∈ Point(dM(I))))
Proof
Definitions occuring in Statement :
dM1: 1,
dM_inc: <x>,
dM: dM(I),
names: names(I),
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
not: ¬A,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
top: Top,
dM_inc: <x>,
dminc: <i>,
free-dl-inc: free-dl-inc(x),
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
DeMorgan-algebra: DeMorganAlgebra,
so_lambda: λ2x.t[x],
and: P ∧ Q,
guard: {T},
uimplies: b supposing a,
so_apply: x[s],
uiff: uiff(P;Q),
empty-fset: {},
fset-null: fset-null(s),
fset-singleton: {x},
all: ∀x:A. B[x]
Lemmas referenced :
dM1-sq-singleton-empty,
dM-point,
equal_wf,
lattice-point_wf,
dM_wf,
subtype_rel_set,
DeMorgan-algebra-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
DeMorgan-algebra-structure-subtype,
subtype_rel_transitivity,
bounded-lattice-structure_wf,
bounded-lattice-axioms_wf,
uall_wf,
lattice-meet_wf,
lattice-join_wf,
DeMorgan-algebra-axioms_wf,
dM_inc_wf,
dM1_wf,
names_wf,
fset_wf,
nat_wf,
member-fset-singleton,
deq-fset_wf,
union-deq_wf,
names-deq_wf,
strong-subtype-deq-subtype,
strong-subtype-union,
strong-subtype-self,
strong-subtype-void,
fset-singleton_wf,
fset-member_wf,
empty-fset_wf,
fset-null_wf,
null_cons_lemma,
null_nil_lemma,
btrue_neq_bfalse
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
sqequalHypSubstitution,
sqequalRule,
extract_by_obid,
isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
applyLambdaEquality,
setElimination,
rename,
imageMemberEquality,
hypothesisEquality,
baseClosed,
imageElimination,
because_Cache,
independent_functionElimination,
applyEquality,
instantiate,
lambdaEquality,
productEquality,
independent_isectElimination,
cumulativity,
universeEquality,
dependent_functionElimination,
unionEquality,
inlEquality,
productElimination,
equalitySymmetry,
hyp_replacement
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[x:names(I)]. (\mneg{}(<x> = 1))
Date html generated:
2017_10_05-AM-00_59_17
Last ObjectModification:
2017_07_28-AM-09_25_15
Theory : cubical!type!theory
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