Nuprl Lemma : name-morph-flip_wf
∀[I:Cname List]. ∀[y:nameset(I)]. ∀[f:name-morph(I;[])]. (flip(f;y) ∈ 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,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
name-morph-flip: flip(f;y),
name-morph: name-morph(I;J),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
nameset: nameset(L),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
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,
int_seg: {i..j-},
lelt: i ≤ j < k,
coordinate_name: Cname,
int_upper: {i...},
squash: ↓T,
sq_stable: SqStable(P),
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top
Lemmas referenced :
name-morph_wf,
nil_wf,
coordinate_name_wf,
nameset_wf,
list_wf,
int_seg_wf,
name-morph-nil,
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,
ext-eq_inversion,
subtype_rel_weakening,
subtract_wf,
int_seg_properties,
sq_stable__le,
sq_stable__l_member,
decidable__equal-coordinate_name,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
intformless_wf,
intformeq_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_wf,
decidable__lt,
lelt_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
because_Cache,
setElimination,
rename,
functionExtensionality,
applyEquality,
functionEquality,
natural_numberEquality,
lambdaFormation,
lambdaEquality,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
dependent_set_memberEquality,
independent_pairFormation,
applyLambdaEquality,
imageMemberEquality,
baseClosed,
imageElimination,
int_eqEquality,
intEquality,
voidEquality,
computeAll
Latex:
\mforall{}[I:Cname List]. \mforall{}[y:nameset(I)]. \mforall{}[f:name-morph(I;[])]. (flip(f;y) \mmember{} name-morph(I;[]))
Date html generated:
2017_10_05-AM-10_10_52
Last ObjectModification:
2017_07_28-AM-11_17_40
Theory : cubical!sets
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