Nuprl Lemma : dM-lift-nc-0
∀J:fset(ℕ). ∀j:{i:ℕ| ¬i ∈ J} . ∀v:Point(dM(J)). ((dM-lift(J;J+j;(j0)) v) = v ∈ Point(dM(J)))
Proof
Definitions occuring in Statement :
nc-0: (i0),
add-name: I+i,
dM-lift: dM-lift(I;J;f),
dM: dM(I),
fset-member: a ∈ s,
fset: fset(T),
int-deq: IntDeq,
nat: ℕ,
all: ∀x:A. B[x],
not: ¬A,
set: {x:A| B[x]} ,
apply: f a,
equal: s = t ∈ T,
lattice-point: Point(l)
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
DeMorgan-algebra: DeMorganAlgebra,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
guard: {T},
uimplies: b supposing a,
so_apply: x[s],
not: ¬A,
implies: P ⇒ Q,
nat: ℕ,
false: False,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
nc-0: (i0),
names: names(I),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
true: True,
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
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,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
DeMorgan-algebra-axioms_wf,
istype-nat,
fset-member_wf,
nat_wf,
int-deq_wf,
strong-subtype-deq-subtype,
strong-subtype-set3,
le_wf,
istype-int,
strong-subtype-self,
istype-void,
fset_wf,
f-subset-add-name,
add-name_wf,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
istype-le,
f-subset_wf,
nc-0_wf,
eq_int_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
dM_inc_wf,
names_wf,
squash_wf,
true_wf,
istype-universe,
dM-lift-is-id,
subtype_rel_self,
iff_weakening_equal,
int_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
sqequalRule,
instantiate,
lambdaEquality_alt,
productEquality,
cumulativity,
because_Cache,
independent_isectElimination,
isectEquality,
setIsType,
functionIsType,
intEquality,
natural_numberEquality,
dependent_functionElimination,
setElimination,
rename,
dependent_set_memberEquality_alt,
unionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
int_eqEquality,
Error :memTop,
independent_pairFormation,
voidElimination,
inhabitedIsType,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
equalityIstype,
promote_hyp,
imageElimination,
universeEquality,
imageMemberEquality,
baseClosed
Latex:
\mforall{}J:fset(\mBbbN{}). \mforall{}j:\{i:\mBbbN{}| \mneg{}i \mmember{} J\} . \mforall{}v:Point(dM(J)). ((dM-lift(J;J+j;(j0)) v) = v)
Date html generated:
2020_05_20-PM-01_36_33
Last ObjectModification:
2020_01_06-PM-00_03_37
Theory : cubical!type!theory
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