Nuprl Lemma : same-binding-trans
∀[vs,ws,us:varname() List]. ∀[v,w,u:varname()].
  ((↑same-binding(vs;ws;v;w)) 
⇒ (↑same-binding(ws;us;w;u)) 
⇒ (↑same-binding(vs;us;v;u)))
Proof
Definitions occuring in Statement : 
same-binding: same-binding(vs;ws;v;w)
, 
varname: varname()
, 
list: T List
, 
assert: ↑b
, 
uall: ∀[x:A]. B[x]
, 
implies: P 
⇒ Q
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
all: ∀x:A. B[x]
, 
nat: ℕ
, 
implies: P 
⇒ Q
, 
false: False
, 
ge: i ≥ j 
, 
uimplies: b supposing a
, 
not: ¬A
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
and: P ∧ Q
, 
prop: ℙ
, 
guard: {T}
, 
or: P ∨ Q
, 
same-binding: same-binding(vs;ws;v;w)
, 
nil: []
, 
it: ⋅
, 
uiff: uiff(P;Q)
, 
rev_uimplies: rev_uimplies(P;Q)
, 
cons: [a / b]
, 
colength: colength(L)
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
sq_type: SQType(T)
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
assert: ↑b
, 
ifthenelse: if b then t else f fi 
, 
bfalse: ff
, 
decidable: Dec(P)
, 
le: A ≤ B
, 
less_than': less_than'(a;b)
, 
less_than: a < b
, 
squash: ↓T
, 
subtype_rel: A ⊆r B
, 
bool: 𝔹
, 
band: p ∧b q
, 
unit: Unit
, 
btrue: tt
, 
bnot: ¬bb
, 
rev_implies: P 
⇐ Q
, 
iff: P 
⇐⇒ Q
, 
cand: A c∧ B
, 
true: True
Lemmas referenced : 
nat_properties, 
full-omega-unsat, 
intformand_wf, 
intformle_wf, 
itermConstant_wf, 
itermVar_wf, 
intformless_wf, 
istype-int, 
int_formula_prop_and_lemma, 
int_formula_prop_le_lemma, 
int_term_value_constant_lemma, 
int_term_value_var_lemma, 
int_formula_prop_less_lemma, 
int_formula_prop_wf, 
ge_wf, 
istype-less_than, 
assert_witness, 
intformeq_wf, 
int_formula_prop_eq_lemma, 
varname_wf, 
list-cases, 
assert-eq_var, 
istype-assert, 
eq_var_wf, 
product_subtype_list, 
colength-cons-not-zero, 
same-binding_wf, 
nil_wf, 
subtract-1-ge-0, 
subtype_base_sq, 
set_subtype_base, 
int_subtype_base, 
spread_cons_lemma, 
istype-void, 
istype-nat, 
colength_wf_list, 
decidable__le, 
intformnot_wf, 
int_formula_prop_not_lemma, 
istype-le, 
list_wf, 
decidable__equal_int, 
subtract_wf, 
itermSubtract_wf, 
itermAdd_wf, 
int_term_value_subtract_lemma, 
int_term_value_add_lemma, 
le_wf, 
cons_wf, 
bnot_wf, 
bool_cases, 
bool_wf, 
bool_subtype_base, 
eqtt_to_assert, 
band_wf, 
btrue_wf, 
bfalse_wf, 
istype-true, 
eqff_to_assert, 
bool_cases_sqequal, 
assert-bnot, 
iff_weakening_uiff, 
assert_wf, 
equal_wf, 
iff_transitivity, 
not_wf, 
assert_of_band, 
assert_of_bnot
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
introduction, 
cut, 
thin, 
lambdaFormation_alt, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
hypothesisEquality, 
hypothesis, 
setElimination, 
rename, 
intWeakElimination, 
natural_numberEquality, 
independent_isectElimination, 
approximateComputation, 
independent_functionElimination, 
dependent_pairFormation_alt, 
lambdaEquality_alt, 
int_eqEquality, 
dependent_functionElimination, 
Error :memTop, 
sqequalRule, 
independent_pairFormation, 
universeIsType, 
voidElimination, 
isect_memberEquality_alt, 
equalityTransitivity, 
equalitySymmetry, 
applyLambdaEquality, 
functionIsTypeImplies, 
inhabitedIsType, 
isectIsTypeImplies, 
unionElimination, 
because_Cache, 
productElimination, 
promote_hyp, 
hypothesis_subsumption, 
equalityIstype, 
instantiate, 
dependent_set_memberEquality_alt, 
imageElimination, 
baseApply, 
closedConclusion, 
baseClosed, 
applyEquality, 
intEquality, 
sqequalBase, 
cumulativity, 
equalityElimination, 
productEquality, 
functionIsType, 
productIsType
Latex:
\mforall{}[vs,ws,us:varname()  List].  \mforall{}[v,w,u:varname()].
    ((\muparrow{}same-binding(vs;ws;v;w))  {}\mRightarrow{}  (\muparrow{}same-binding(ws;us;w;u))  {}\mRightarrow{}  (\muparrow{}same-binding(vs;us;v;u)))
Date html generated:
2020_05_19-PM-09_53_10
Last ObjectModification:
2020_03_09-PM-04_08_00
Theory : terms
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