Nuprl Lemma : A-shift-upto_wf
∀[Val:Type]. ∀[n:ℕ].  (1 < n 
⇒ (∀[AType:array{i:l}(Val;n)]. ∀[j:ℕn].  (A-shift-upto(AType;j) ∈ A-map Unit)))
Proof
Definitions occuring in Statement : 
A-shift-upto: A-shift-upto(AType;j)
, 
A-map: A-map
, 
array-model: array-model(AType)
, 
array: array{i:l}(Val;n)
, 
int_seg: {i..j-}
, 
nat: ℕ
, 
less_than: a < b
, 
uall: ∀[x:A]. B[x]
, 
implies: P 
⇒ Q
, 
unit: Unit
, 
member: t ∈ T
, 
apply: f a
, 
natural_number: $n
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
implies: P 
⇒ Q
, 
A-shift-upto: A-shift-upto(AType;j)
, 
let: let, 
all: ∀x:A. B[x]
, 
int_seg: {i..j-}
, 
lelt: i ≤ j < k
, 
and: P ∧ Q
, 
le: A ≤ B
, 
less_than': less_than'(a;b)
, 
false: False
, 
not: ¬A
, 
prop: ℙ
, 
nat: ℕ
, 
subtype_rel: A ⊆r B
, 
guard: {T}
, 
ge: i ≥ j 
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
uimplies: b supposing a
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
top: Top
Lemmas referenced : 
A-bind_wf, 
unit_wf2, 
nat_wf, 
less_than_wf, 
array_wf, 
int_seg_wf, 
int_term_value_subtract_lemma, 
itermSubtract_wf, 
subtract_wf, 
A-assign_wf, 
int_formula_prop_less_lemma, 
intformless_wf, 
decidable__lt, 
int_formula_prop_wf, 
int_term_value_var_lemma, 
int_term_value_constant_lemma, 
int_formula_prop_le_lemma, 
int_formula_prop_not_lemma, 
int_formula_prop_and_lemma, 
itermVar_wf, 
itermConstant_wf, 
intformle_wf, 
intformnot_wf, 
intformand_wf, 
satisfiable-full-omega-tt, 
decidable__le, 
nat_properties, 
int_seg_properties, 
A-fetch'_wf, 
A-coerce_wf, 
lelt_wf, 
false_wf, 
A-loop_wf2
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
lambdaFormation, 
sqequalRule, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
cumulativity, 
hypothesisEquality, 
dependent_functionElimination, 
dependent_set_memberEquality, 
natural_numberEquality, 
independent_pairFormation, 
hypothesis, 
setElimination, 
rename, 
lambdaEquality, 
applyEquality, 
because_Cache, 
productElimination, 
unionElimination, 
independent_isectElimination, 
dependent_pairFormation, 
int_eqEquality, 
intEquality, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
computeAll, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
universeEquality
Latex:
\mforall{}[Val:Type].  \mforall{}[n:\mBbbN{}].
    (1  <  n  {}\mRightarrow{}  (\mforall{}[AType:array\{i:l\}(Val;n)].  \mforall{}[j:\mBbbN{}n].    (A-shift-upto(AType;j)  \mmember{}  A-map  Unit)))
Date html generated:
2016_05_15-PM-02_21_19
Last ObjectModification:
2016_01_15-PM-00_17_55
Theory : monads
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