Nuprl Lemma : dM-lift-dMpair
∀[I,J:fset(ℕ)]. ∀[f:J ⟶ I]. ∀[x,y:names(I)].  ((dM-lift(J;I;f) dMpair(x;y)) = f x ∧ f y ∈ Point(dM(J)))
Proof
Definitions occuring in Statement : 
dM-lift: dM-lift(I;J;f)
, 
names-hom: I ⟶ J
, 
dMpair: dMpair(i;j)
, 
dM: dM(I)
, 
names: names(I)
, 
lattice-meet: a ∧ b
, 
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
, 
names: names(I)
, 
uimplies: b supposing a
, 
subtype_rel: A ⊆r B
, 
nat: ℕ
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
sq_stable: SqStable(P)
, 
implies: P 
⇒ Q
, 
squash: ↓T
, 
all: ∀x:A. B[x]
, 
names-hom: I ⟶ J
, 
prop: ℙ
, 
DeMorgan-algebra: DeMorganAlgebra
, 
and: P ∧ Q
, 
guard: {T}
, 
dma-hom: dma-hom(dma1;dma2)
, 
true: True
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
bounded-lattice-hom: Hom(l1;l2)
, 
lattice-hom: Hom(l1;l2)
Lemmas referenced : 
dMpair-eq-meet, 
sq_stable__fset-member, 
nat_wf, 
int-deq_wf, 
strong-subtype-deq-subtype, 
strong-subtype-set3, 
le_wf, 
istype-int, 
strong-subtype-self, 
names_wf, 
names-hom_wf, 
fset_wf, 
dM-lift_wf, 
equal_wf, 
squash_wf, 
true_wf, 
istype-universe, 
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, 
lattice-hom-meet, 
bdd-distributive-lattice-subtype-bdd-lattice, 
DeMorgan-algebra-subtype, 
DeMorgan-algebra_wf, 
bdd-distributive-lattice_wf, 
bdd-lattice_wf, 
dM_inc_wf, 
subtype_rel_self, 
iff_weakening_equal
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
introduction, 
cut, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
setElimination, 
rename, 
hypothesis, 
independent_isectElimination, 
applyEquality, 
intEquality, 
because_Cache, 
sqequalRule, 
lambdaEquality_alt, 
natural_numberEquality, 
independent_functionElimination, 
imageMemberEquality, 
baseClosed, 
imageElimination, 
inhabitedIsType, 
isect_memberEquality_alt, 
axiomEquality, 
isectIsTypeImplies, 
universeIsType, 
lambdaFormation_alt, 
equalityIstype, 
equalityTransitivity, 
equalitySymmetry, 
dependent_functionElimination, 
instantiate, 
universeEquality, 
productEquality, 
cumulativity, 
productElimination, 
hyp_replacement, 
applyLambdaEquality
Latex:
\mforall{}[I,J:fset(\mBbbN{})].  \mforall{}[f:J  {}\mrightarrow{}  I].  \mforall{}[x,y:names(I)].    ((dM-lift(J;I;f)  dMpair(x;y))  =  f  x  \mwedge{}  f  y)
Date html generated:
2019_11_04-PM-05_30_46
Last ObjectModification:
2018_12_13-AM-10_02_48
Theory : cubical!type!theory
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