Nuprl Lemma : name-morph-flips-commute
∀I:Cname List. ∀x:name-morph(I;[]). ∀i,j:nameset(I). (flip(flip(x;j);i) = flip(flip(x;i);j) ∈ 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 ,
name-morph: name-morph(I;J),
subtype_rel: A ⊆r B,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
coordinate_name: Cname,
int_upper: {i...},
squash: ↓T,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
sq_stable: SqStable(P),
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
name-morph-ext,
nil_wf,
coordinate_name_wf,
name-morph-flip_wf,
name-morph_wf,
eq-cname_wf,
bool_wf,
eqtt_to_assert,
assert-eq-cname,
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,
equal_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
set_subtype_base,
int_subtype_base,
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,
because_Cache,
sqequalRule,
setElimination,
rename,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
applyEquality,
natural_numberEquality,
applyLambdaEquality,
imageMemberEquality,
baseClosed,
imageElimination,
dependent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
dependent_set_memberEquality,
independent_pairFormation,
independent_functionElimination,
promote_hyp,
instantiate,
cumulativity
Latex:
\mforall{}I:Cname List. \mforall{}x:name-morph(I;[]). \mforall{}i,j:nameset(I). (flip(flip(x;j);i) = flip(flip(x;i);j))
Date html generated:
2017_10_05-AM-10_10_57
Last ObjectModification:
2017_07_28-AM-11_17_42
Theory : cubical!sets
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