Nuprl Lemma : A-shift-upto-spec_wf
∀[Val:Type]. ∀[n:ℕ]. ∀[AType:array{i:l}(Val;n)]. ∀[prog:A-map Unit]. ∀[j:ℕn].
(A-shift-upto-spec(AType; Val; n; prog; j) ∈ ℙ)
Proof
Definitions occuring in Statement :
A-shift-upto-spec: A-shift-upto-spec(AType; Val; n; prog; j),
A-map: A-map,
array-model: array-model(AType),
array: array{i:l}(Val;n),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
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,
A-shift-upto-spec: A-shift-upto-spec(AType; Val; n; prog; j),
so_lambda: λ2x.t[x],
nat: ℕ,
int_seg: {i..j-},
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
lelt: i ≤ j < k,
guard: {T},
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
subtract: n - m,
prop: ℙ,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
so_apply: x[s]
Lemmas referenced :
all_wf,
Arr_wf,
int_seg_wf,
lt_int_wf,
subtract_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
equal_wf,
A-post-val_wf,
A-pre-val_wf,
add-member-int_seg2,
int_seg_properties,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermSubtract_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
lelt_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
less_than_wf,
A-map_wf,
unit_wf2,
array_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
lambdaEquality,
natural_numberEquality,
setElimination,
rename,
because_Cache,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
dependent_set_memberEquality,
independent_pairFormation,
dependent_functionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
instantiate,
independent_functionElimination,
axiomEquality,
applyEquality,
universeEquality
Latex:
\mforall{}[Val:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[AType:array\{i:l\}(Val;n)]. \mforall{}[prog:A-map Unit]. \mforall{}[j:\mBbbN{}n].
(A-shift-upto-spec(AType; Val; n; prog; j) \mmember{} \mBbbP{})
Date html generated:
2017_10_01-AM-08_44_49
Last ObjectModification:
2017_07_26-PM-04_30_21
Theory : monads
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