Nuprl Lemma : dM-lift-s
∀[I,J:fset(ℕ)]. ∀[x:Point(dM(I))]. ((dM-lift(J;I;s) x) = x ∈ Point(dM(J))) supposing I ⊆ J
Proof
Definitions occuring in Statement :
nc-s: s,
dM-lift: dM-lift(I;J;f),
dM: dM(I),
lattice-point: Point(l),
f-subset: xs ⊆ ys,
fset: fset(T),
int-deq: IntDeq,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
apply: f a,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
subtype_rel: A ⊆r B,
prop: ℙ,
all: ∀x:A. B[x],
nc-s: s,
dM_inc: <x>,
dminc: <i>,
free-dl-inc: free-dl-inc(x),
fset-singleton: {x},
cons: [a / b],
DeMorgan-algebra: DeMorganAlgebra,
so_lambda: λ2x.t[x],
and: P ∧ Q,
guard: {T},
so_apply: x[s],
nat: ℕ,
f-subset: xs ⊆ ys,
implies: P ⇒ Q
Lemmas referenced :
dM-lift-is-id2,
f-subset_wf,
nat_wf,
int-deq_wf,
nc-s_wf,
dM_inc_wf,
names-subtype,
names_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,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
DeMorgan-algebra-axioms_wf,
strong-subtype-deq-subtype,
strong-subtype-set3,
le_wf,
strong-subtype-self,
fset_wf,
fset-member_witness,
fset-member_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_set_memberEquality,
hypothesis,
applyEquality,
because_Cache,
sqequalRule,
independent_isectElimination,
lambdaFormation,
instantiate,
lambdaEquality,
productEquality,
cumulativity,
universeEquality,
intEquality,
natural_numberEquality,
introduction,
independent_functionElimination
Latex:
\mforall{}[I,J:fset(\mBbbN{})]. \mforall{}[x:Point(dM(I))]. ((dM-lift(J;I;s) x) = x) supposing I \msubseteq{} J
Date html generated:
2016_05_18-PM-00_00_34
Last ObjectModification:
2015_12_28-PM-03_06_15
Theory : cubical!type!theory
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