Nuprl Lemma : dM-lift-opp
∀[I,J:fset(ℕ)]. ∀[f:I ⟶ J]. ∀[x:names(J)]. ((dM-lift(I;J;f) <1-x>) = ¬(f x) ∈ Point(dM(I)))
Proof
Definitions occuring in Statement :
dM-lift: dM-lift(I;J;f),
names-hom: I ⟶ J,
dM_opp: <1-x>,
dM: dM(I),
names: names(I),
dma-neg: ¬(x),
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
apply: f a,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
DeMorgan-algebra: DeMorganAlgebra,
prop: ℙ,
and: P ∧ Q,
guard: {T},
uimplies: b supposing a,
so_apply: x[s],
dma-hom: dma-hom(dma1;dma2),
bounded-lattice-hom: Hom(l1;l2),
lattice-hom: Hom(l1;l2),
names-hom: I ⟶ J,
implies: P ⇒ Q,
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
dM: dM(I),
dma-neg: ¬(x),
free-DeMorgan-algebra: free-DeMorgan-algebra(T;eq),
mk-DeMorgan-algebra: mk-DeMorgan-algebra(L;n),
top: Top,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt
Lemmas referenced :
dM-lift_wf,
set_wf,
dma-hom_wf,
dM_wf,
all_wf,
names_wf,
equal_wf,
lattice-point_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,
names-hom_wf,
fset_wf,
nat_wf,
squash_wf,
true_wf,
neg-dM_inc,
dma-neg_wf,
DeMorgan-algebra_wf,
iff_weakening_equal,
rec_select_update_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
sqequalRule,
lambdaEquality,
because_Cache,
applyEquality,
instantiate,
productEquality,
independent_isectElimination,
cumulativity,
universeEquality,
setElimination,
rename,
lambdaFormation,
productElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
isect_memberEquality,
axiomEquality,
imageElimination,
equalityUniverse,
levelHypothesis,
natural_numberEquality,
imageMemberEquality,
baseClosed,
voidElimination,
voidEquality
Latex:
\mforall{}[I,J:fset(\mBbbN{})]. \mforall{}[f:I {}\mrightarrow{} J]. \mforall{}[x:names(J)]. ((dM-lift(I;J;f) ə-x>) = \mneg{}(f x))
Date html generated:
2017_10_05-AM-00_59_48
Last ObjectModification:
2017_07_28-AM-09_25_34
Theory : cubical!type!theory
Home
Index