Nuprl Lemma : rename-one-name_wf
∀[I:Cname List]. ∀[z1,z2:Cname].
rename-one-name(z1;z2) ∈ name-morph([z1 / I];[z2 / I]) supposing (¬(z1 ∈ I)) ∧ (¬(z2 ∈ I))
Proof
Definitions occuring in Statement :
rename-one-name: rename-one-name(z1;z2),
name-morph: name-morph(I;J),
coordinate_name: Cname,
l_member: (x ∈ l),
cons: [a / b],
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
and: P ∧ Q,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
rename-one-name: rename-one-name(z1;z2),
and: P ∧ Q,
name-morph: name-morph(I;J),
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
false: False,
assert: ↑b,
bnot: ¬bb,
guard: {T},
sq_type: SQType(T),
or: P ∨ Q,
exists: ∃x:A. B[x],
bfalse: ff,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
all: ∀x:A. B[x],
nameset: nameset(L),
subtype_rel: A ⊆r B,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
coordinate_name: Cname,
int_upper: {i...},
isname: isname(z),
true: True,
so_lambda: λ2x.t[x],
so_apply: x[s],
squash: ↓T,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
decidable: Dec(P)
Lemmas referenced :
l_member_wf,
coordinate_name_wf,
istype-void,
list_wf,
cons_wf,
nameset_wf,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
assert-eq-cname,
eqtt_to_assert,
bool_wf,
eq-cname_wf,
nameset_subtype_extd-nameset,
cons_member,
iff_imp_equal_bool,
le_int_wf,
btrue_wf,
iff_functionality_wrt_iff,
assert_wf,
le_wf,
true_wf,
iff_weakening_uiff,
assert_of_le_int,
iff_weakening_equal,
equal-wf-T-base,
set_subtype_base,
istype-int,
int_subtype_base,
isname-nameset,
extd-nameset_wf,
nameset_subtype_base,
extd-nameset_subtype_base,
full-omega-unsat,
intformnot_wf,
intformeq_wf,
itermVar_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
decidable__equal_int,
int_formula_prop_wf,
istype-le,
istype-assert,
isname_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
dependent_set_memberEquality_alt,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
productIsType,
functionIsType,
universeIsType,
extract_by_obid,
isectElimination,
hypothesisEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
voidElimination,
because_Cache,
independent_functionElimination,
cumulativity,
instantiate,
dependent_functionElimination,
promote_hyp,
dependent_pairFormation,
independent_isectElimination,
equalityElimination,
unionElimination,
lambdaFormation,
rename,
setElimination,
lambdaEquality,
applyEquality,
dependent_set_memberEquality,
inlFormation,
inrFormation,
lambdaFormation_alt,
natural_numberEquality,
independent_pairFormation,
dependent_pairFormation_alt,
equalityIsType3,
intEquality,
lambdaEquality_alt,
closedConclusion,
equalityIsType1,
inlFormation_alt,
equalityIsType4,
applyLambdaEquality,
imageMemberEquality,
baseClosed,
imageElimination,
approximateComputation,
int_eqEquality
Latex:
\mforall{}[I:Cname List]. \mforall{}[z1,z2:Cname].
rename-one-name(z1;z2) \mmember{} name-morph([z1 / I];[z2 / I]) supposing (\mneg{}(z1 \mmember{} I)) \mwedge{} (\mneg{}(z2 \mmember{} I))
Date html generated:
2019_11_05-PM-00_25_01
Last ObjectModification:
2018_11_08-PM-00_27_38
Theory : cubical!sets
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