Nuprl Lemma : mkW_wf
∀[Pos:Type]. ∀[Mv:Pos ⟶ Type]. ∀[a:Pos]. ∀[f:Mv[a] ⟶ WfdSpread(Pos;a.Mv[a])]. (mkW(a;f) ∈ WfdSpread(Pos;a.Mv[a]))
Proof
Definitions occuring in Statement :
mkW: mkW(a;f),
WfdSpread: WfdSpread(Pos;a.Mv[a]),
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mkW: mkW(a;f),
WfdSpread: WfdSpread(Pos;a.Mv[a]),
all: ∀x:A. B[x],
squash: ↓T,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
nat: ℕ,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
exists: ∃x:A. B[x],
ext-eq: A ≡ B,
subgame: subgame(g;p;n),
resigned: resigned(x),
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
isr: isr(x),
assert: ↑b,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
subtract: n - m,
nequal: a ≠ b ∈ T ,
int_seg: {i..j-},
lelt: i ≤ j < k,
true: True,
int_upper: {i...},
eq_int: (i =z j)
Lemmas referenced :
spread-ext,
nat_wf,
MoveChoice_wf,
all_wf,
squash_wf,
exists_wf,
resigned_wf,
subgame_wf,
subtype_rel_dep_function,
int_seg_wf,
int_seg_subtype_nat,
false_wf,
subtype_rel_self,
WfdSpread_wf,
Spread_wf,
le_wf,
unit_wf2,
equal_wf,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
intformeq_wf,
int_formula_prop_eq_lemma,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
add-associates,
add-swap,
add-commutes,
zero-add,
true_wf,
add-subtract-cancel,
int_seg_properties,
and_wf,
isr_wf,
assert_elim,
int_upper_subtype_nat,
nequal-le-implies,
assert_wf,
subtract_wf,
int_upper_properties,
itermSubtract_wf,
int_term_value_subtract_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
dependent_set_memberEquality,
lambdaFormation,
hypothesis,
imageElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
functionEquality,
cumulativity,
lambdaEquality,
applyEquality,
functionExtensionality,
natural_numberEquality,
setElimination,
rename,
independent_isectElimination,
independent_pairFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality,
dependent_pairEquality,
productElimination,
unionEquality,
unionElimination,
dependent_functionElimination,
independent_functionElimination,
applyLambdaEquality,
addEquality,
dependent_pairFormation,
int_eqEquality,
intEquality,
voidElimination,
voidEquality,
computeAll,
equalityElimination,
promote_hyp,
instantiate,
hypothesis_subsumption
Latex:
\mforall{}[Pos:Type]. \mforall{}[Mv:Pos {}\mrightarrow{} Type]. \mforall{}[a:Pos]. \mforall{}[f:Mv[a] {}\mrightarrow{} WfdSpread(Pos;a.Mv[a])].
(mkW(a;f) \mmember{} WfdSpread(Pos;a.Mv[a]))
Date html generated:
2017_04_17-AM-09_28_47
Last ObjectModification:
2017_02_27-PM-05_28_58
Theory : spread
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