Nuprl Lemma : name-morph-flip-id
∀I:Cname List. ∀x:nameset(I). ∀c2:cat-ob(poset-cat(I)). (c2 = flip(c2;x) ∈ cat-ob(poset-cat(I-[x])))
Proof
Definitions occuring in Statement :
poset-cat: poset-cat(J),
name-morph-flip: flip(f;y),
nameset: nameset(L),
cname_deq: CnameDeq,
coordinate_name: Cname,
cat-ob: cat-ob(C),
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],
poset-cat: poset-cat(J),
cat-ob: cat-ob(C),
pi1: fst(t),
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
nameset: nameset(L),
subtype_rel: A ⊆r B,
name-morph-flip: flip(f;y),
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
name-morph: name-morph(I;J),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
coordinate_name: Cname,
int_upper: {i...},
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
cat-ob_wf,
poset-cat_wf,
nameset_wf,
list_wf,
coordinate_name_wf,
name-morph-ext,
list-diff_wf,
cname_deq_wf,
cons_wf,
nil_wf,
name-morph_subtype,
nameset_subtype,
list-diff-subset,
name-morph-flip_wf,
eq-cname_wf,
bool_wf,
eqtt_to_assert,
assert-eq-cname,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
member-list-diff,
member_singleton,
set_subtype_base,
le_wf,
int_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
sqequalHypSubstitution,
hypothesis,
introduction,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
setElimination,
rename,
applyEquality,
because_Cache,
lambdaEquality,
dependent_functionElimination,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
dependent_pairFormation,
promote_hyp,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
independent_pairFormation,
intEquality,
natural_numberEquality
Latex:
\mforall{}I:Cname List. \mforall{}x:nameset(I). \mforall{}c2:cat-ob(poset-cat(I)). (c2 = flip(c2;x))
Date html generated:
2017_10_05-AM-10_29_26
Last ObjectModification:
2017_07_28-AM-11_24_16
Theory : cubical!sets
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