Nuprl Lemma : nc-m_wf
∀[I:fset(ℕ)]. ∀[i,j:ℕ]. m(i;j) ∈ I+j ⟶ I supposing i ∈ I
Proof
Definitions occuring in Statement :
nc-m: m(i;j),
add-name: I+i,
names-hom: I ⟶ J,
fset-member: a ∈ s,
fset: fset(T),
int-deq: IntDeq,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
names-hom: I ⟶ J,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
nc-m: m(i;j),
names: names(I),
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
guard: {T},
or: P ∨ Q,
prop: ℙ,
bfalse: ff,
exists: ∃x:A. B[x],
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
false: False,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
dMpair_wf,
add-name_wf,
fset-member-add-name,
equal_wf,
trivial-member-add-name1,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
dM_inc_wf,
names-subtype,
f-subset-add-name,
names_wf,
fset-member_wf,
nat_wf,
int-deq_wf,
strong-subtype-deq-subtype,
strong-subtype-set3,
le_wf,
strong-subtype-self,
fset_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
because_Cache,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
hypothesisEquality,
dependent_functionElimination,
inrFormation,
intEquality,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation,
promote_hyp,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
applyEquality,
axiomEquality,
natural_numberEquality,
isect_memberEquality
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[i,j:\mBbbN{}]. m(i;j) \mmember{} I+j {}\mrightarrow{} I supposing i \mmember{} I
Date html generated:
2017_10_05-AM-01_03_05
Last ObjectModification:
2017_07_28-AM-09_26_34
Theory : cubical!type!theory
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