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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