Nuprl Lemma : add-remove-fresh-cname
∀I:Cname List. (I = [fresh-cname(I) / I]-[fresh-cname(I)] ∈ (Cname List))
Proof
Definitions occuring in Statement :
fresh-cname: fresh-cname(I),
cname_deq: CnameDeq,
coordinate_name: Cname,
list-diff: as-bs,
cons: [a / b],
nil: [],
list: T List,
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
top: Top,
deq: EqDecider(T),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
list_wf,
coordinate_name_wf,
fresh-cname_wf,
set_wf,
not_wf,
l_member_wf,
equal_wf,
squash_wf,
true_wf,
list-diff-cons,
cname_deq_wf,
cons_wf,
nil_wf,
iff_weakening_equal,
deq_member_cons_lemma,
deq_member_nil_lemma,
bor_wf,
deq_wf,
bfalse_wf,
bool_wf,
eqtt_to_assert,
assert-deq-member,
strong-subtype-deq-subtype,
strong-subtype-set2,
eqff_to_assert,
deq-member_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
list-diff-disjoint,
l_disjoint_singleton,
cons_member
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
applyEquality,
imageElimination,
universeEquality,
because_Cache,
setElimination,
rename,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
isect_memberEquality,
voidElimination,
voidEquality,
unionElimination,
equalityElimination,
setEquality,
dependent_set_memberEquality,
dependent_pairFormation,
promote_hyp,
instantiate,
cumulativity,
inlFormation
Latex:
\mforall{}I:Cname List. (I = [fresh-cname(I) / I]-[fresh-cname(I)])
Date html generated:
2017_10_05-AM-10_05_16
Last ObjectModification:
2017_07_28-AM-11_16_00
Theory : cubical!sets
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