Nuprl Lemma : name-morph-flip-face-map1
∀I:Cname List. ∀y:nameset(I). ∀a:ℕ2. ∀f:name-morph(I-[y];[]). ∀v:nameset(I).
((¬(v = y ∈ Cname)) ⇒ (flip(((y:=a) o f);v) = ((y:=a) o flip(f;v)) ∈ name-morph(I;[])))
Proof
Definitions occuring in Statement :
name-morph-flip: flip(f;y),
name-comp: (f o g),
face-map: (x:=i),
name-morph: name-morph(I;J),
nameset: nameset(L),
cname_deq: CnameDeq,
coordinate_name: Cname,
list-diff: as-bs,
cons: [a / b],
nil: [],
list: T List,
int_seg: {i..j-},
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
nameset: nameset(L),
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B,
not: ¬A,
prop: ℙ,
false: False,
guard: {T},
uimplies: b supposing a,
name-morph-flip: flip(f;y),
face-map: (x:=i),
name-comp: (f o g),
compose: f o g,
uext: uext(g),
coordinate_name: Cname,
int_upper: {i...},
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
decidable: Dec(P),
or: P ∨ Q,
sq_type: SQType(T),
isname: isname(z),
le_int: i ≤z j,
lt_int: i <z j,
bnot: ¬bb,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
bfalse: ff,
squash: ↓T,
less_than: a < b,
top: Top,
assert: ↑b,
subtype_rel: A ⊆r B,
name-morph: name-morph(I;J),
nequal: a ≠ b ∈ T
Lemmas referenced :
member-list-diff,
coordinate_name_wf,
cname_deq_wf,
cons_wf,
nil_wf,
member_singleton,
l_member_wf,
list-diff_wf,
istype-void,
name-morph-ext,
name-morph-flip_wf,
name-comp_wf,
face-map_wf2,
name-morph_wf,
int_seg_wf,
nameset_wf,
list_wf,
eq_int_wf,
eqtt_to_assert,
assert_of_eq_int,
decidable__equal_int,
subtype_base_sq,
int_subtype_base,
int_seg_properties,
int_seg_subtype_special,
int_seg_cases,
full-omega-unsat,
intformand_wf,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
eq-cname_wf,
assert-eq-cname,
intformeq_wf,
intformnot_wf,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
istype-le,
eqff_to_assert,
bool_cases_sqequal,
bool_wf,
bool_subtype_base,
assert-bnot,
iff_weakening_uiff,
assert_wf,
equal_wf,
nsub2_subtype_extd-nameset,
neg_assert_of_eq_int,
subtract_wf,
decidable__le,
itermSubtract_wf,
int_term_value_subtract_lemma,
decidable__lt,
istype-less_than,
isname-name
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality_alt,
hypothesisEquality,
introduction,
extract_by_obid,
isectElimination,
hypothesis,
dependent_functionElimination,
because_Cache,
productElimination,
independent_functionElimination,
independent_pairFormation,
universeIsType,
sqequalRule,
functionIsType,
equalityIstype,
independent_isectElimination,
natural_numberEquality,
inhabitedIsType,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
instantiate,
cumulativity,
intEquality,
hypothesis_subsumption,
approximateComputation,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
Error :memTop,
voidElimination,
applyLambdaEquality,
imageMemberEquality,
baseClosed,
imageElimination,
isect_memberEquality_alt,
promote_hyp,
applyEquality,
productIsType
Latex:
\mforall{}I:Cname List. \mforall{}y:nameset(I). \mforall{}a:\mBbbN{}2. \mforall{}f:name-morph(I-[y];[]). \mforall{}v:nameset(I).
((\mneg{}(v = y)) {}\mRightarrow{} (flip(((y:=a) o f);v) = ((y:=a) o flip(f;v))))
Date html generated:
2020_05_21-AM-10_50_01
Last ObjectModification:
2019_12_10-PM-02_23_58
Theory : cubical!sets
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