Nuprl Lemma : name-morph-flip-flip
∀I:Cname List. ∀f:name-morph(I;[]). ∀j:nameset(I). (flip(flip(f;j);j) = f ∈ name-morph(I;[]))
Proof
Definitions occuring in Statement :
name-morph-flip: flip(f;y),
name-morph: name-morph(I;J),
nameset: nameset(L),
coordinate_name: Cname,
nil: [],
list: T List,
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
name-morph-flip: flip(f;y),
nameset: nameset(L),
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,
subtype_rel: A ⊆r B,
name-morph: name-morph(I;J),
int_seg: {i..j-},
lelt: i ≤ j < k,
coordinate_name: Cname,
int_upper: {i...},
squash: ↓T,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
sq_stable: SqStable(P)
Lemmas referenced :
name-morph-ext,
nil_wf,
coordinate_name_wf,
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,
nameset_wf,
name-morph_wf,
list_wf,
extd-nameset-nil,
int_seg_wf,
int_seg_properties,
decidable__equal_int,
subtract_wf,
satisfiable-full-omega-tt,
intformnot_wf,
intformeq_wf,
itermSubtract_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
sq_stable__le,
sq_stable__l_member,
decidable__equal-coordinate_name,
decidable__le,
intformand_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
lelt_wf,
nsub2_subtype_extd-nameset
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
sqequalRule,
setElimination,
rename,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
because_Cache,
voidElimination,
applyEquality,
natural_numberEquality,
applyLambdaEquality,
imageMemberEquality,
baseClosed,
imageElimination,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidEquality,
computeAll,
dependent_set_memberEquality,
independent_pairFormation
Latex:
\mforall{}I:Cname List. \mforall{}f:name-morph(I;[]). \mforall{}j:nameset(I). (flip(flip(f;j);j) = f)
Date html generated:
2017_10_05-AM-10_11_07
Last ObjectModification:
2017_07_28-AM-11_17_46
Theory : cubical!sets
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