Nuprl Lemma : neg-dM_opp
∀[I:fset(ℕ)]. ∀[x:names(I)]. (¬(<1-x>) = <x> ∈ Point(dM(I)))
Proof
Definitions occuring in Statement :
dM_opp: <1-x>,
dM_inc: <x>,
dM: dM(I),
names-deq: NamesDeq,
names: names(I),
dm-neg: ¬(x),
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
dM_inc: <x>,
dM_opp: <1-x>,
dM: dM(I),
top: Top,
squash: ↓T,
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,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
free-dma-point,
equal_wf,
squash_wf,
true_wf,
lattice-point_wf,
free-DeMorgan-lattice_wf,
names_wf,
names-deq_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,
dm-neg-opp,
dminc_wf,
iff_weakening_equal,
fset_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
applyEquality,
lambdaEquality,
imageElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
because_Cache,
instantiate,
productEquality,
cumulativity,
independent_isectElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
axiomEquality
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[x:names(I)]. (\mneg{}(ə-x>) = <x>)
Date html generated:
2017_10_05-AM-00_59_36
Last ObjectModification:
2017_07_28-AM-09_25_24
Theory : cubical!type!theory
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