Nuprl Lemma : permr_upto_wf
∀T:Type. ∀R:T ⟶ T ⟶ ℙ. ∀as,bs:T List.  (as ≡ bs upto x,y.R[x;y]  ∈ ℙ)
Proof
Definitions occuring in Statement : 
permr_upto: as ≡ bs upto x,y.R[x; y] 
, 
list: T List
, 
prop: ℙ
, 
so_apply: x[s1;s2]
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
permr_upto: as ≡ bs upto x,y.R[x; y] 
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
prop: ℙ
, 
cand: A c∧ B
, 
uall: ∀[x:A]. B[x]
, 
sym_grp: Sym(n)
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s1;s2]
, 
perm: Perm(T)
, 
subtype_rel: A ⊆r B
, 
uimplies: b supposing a
, 
ge: i ≥ j 
, 
guard: {T}
, 
int_seg: {i..j-}
, 
lelt: i ≤ j < k
, 
and: P ∧ Q
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
false: False
, 
nat: ℕ
, 
less_than: a < b
, 
squash: ↓T
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
top: Top
, 
so_apply: x[s]
Lemmas referenced : 
equal_wf, 
length_wf, 
exists_wf, 
perm_wf, 
int_seg_wf, 
all_wf, 
select_wf, 
perm_f_wf, 
non_neg_length, 
int_seg_properties, 
decidable__le, 
le_wf, 
less_than_wf, 
length_wf_nat, 
nat_properties, 
full-omega-unsat, 
intformand_wf, 
intformle_wf, 
itermConstant_wf, 
itermVar_wf, 
intformnot_wf, 
istype-int, 
int_formula_prop_and_lemma, 
istype-void, 
int_formula_prop_le_lemma, 
int_term_value_constant_lemma, 
int_term_value_var_lemma, 
int_formula_prop_not_lemma, 
int_formula_prop_wf, 
decidable__lt, 
intformless_wf, 
int_formula_prop_less_lemma, 
intformeq_wf, 
int_formula_prop_eq_lemma, 
list_wf, 
istype-universe
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
lambdaFormation_alt, 
cut, 
productEquality, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
intEquality, 
hypothesisEquality, 
hypothesis, 
because_Cache, 
dependent_functionElimination, 
natural_numberEquality, 
lambdaEquality_alt, 
applyEquality, 
setElimination, 
rename, 
independent_isectElimination, 
equalityTransitivity, 
equalitySymmetry, 
productElimination, 
dependent_set_memberEquality_alt, 
independent_pairFormation, 
productIsType, 
universeIsType, 
unionElimination, 
applyLambdaEquality, 
imageElimination, 
approximateComputation, 
independent_functionElimination, 
dependent_pairFormation_alt, 
int_eqEquality, 
isect_memberEquality_alt, 
voidElimination, 
inhabitedIsType, 
functionIsType, 
universeEquality
Latex:
\mforall{}T:Type.  \mforall{}R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}.  \mforall{}as,bs:T  List.    (as  \mequiv{}  bs  upto  x,y.R[x;y]    \mmember{}  \mBbbP{})
Date html generated:
2019_10_16-PM-01_01_08
Last ObjectModification:
2018_10_08-AM-10_05_54
Theory : perms_2
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