Nuprl Lemma : mk-wfd-tree_wf
∀[A:Type]. ∀[f:A ⟶ wfd-tree(A)]. (mk-wfd-tree(f) ∈ wfd-tree(A))
Proof
Definitions occuring in Statement :
mk-wfd-tree: mk-wfd-tree(f),
wfd-tree2: wfd-tree(A),
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mk-wfd-tree: mk-wfd-tree(f),
subtype_rel: A ⊆r B,
wfd-tree2: wfd-tree(A),
guard: {T},
uimplies: b supposing a,
all: ∀x:A. B[x],
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
w-bars: w-bars(w;p),
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
squash: ↓T,
so_lambda: λ2x.t[x],
so_apply: x[s],
co-w-select: w@s,
co-w-null: co-w-null(w),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
bor: p ∨bq,
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
outr: outr(x),
nat_plus: ℕ+,
nequal: a ≠ b ∈ T ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
subtract: n - m,
true: True,
compose: f o g,
int_seg: {i..j-}
Lemmas referenced :
co-w-ext,
wfd-tree2_wf,
unit_wf2,
ext-eq_inversion,
co-w_wf,
subtype_rel_weakening,
nat_wf,
false_wf,
le_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,
equal_wf,
assert_wf,
co-w-null_wf,
co-w-select_wf,
map_wf,
int_seg_wf,
subtype_rel_dep_function,
int_seg_subtype_nat,
upto_wf,
all_wf,
w-bars_wf,
null-map,
null-upto,
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,
upto_decomp2,
decidable__lt,
not-lt-2,
not-equal-2,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
minus-one-mul-top,
add-commutes,
add_functionality_wrt_le,
add-associates,
add-zero,
le-add-cancel,
less_than_wf,
map_cons_lemma,
reduce_hd_cons_lemma,
reduce_tl_cons_lemma,
map-map,
list_wf,
subtract_wf,
list_subtype_base,
set_subtype_base,
lelt_wf,
int_subtype_base,
squash_wf,
true_wf,
add-swap
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
inrEquality,
functionExtensionality,
applyEquality,
hypothesis,
lambdaEquality,
setElimination,
rename,
cumulativity,
unionEquality,
functionEquality,
independent_isectElimination,
dependent_set_memberEquality,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
natural_numberEquality,
independent_pairFormation,
dependent_functionElimination,
because_Cache,
addEquality,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
imageElimination,
imageMemberEquality,
baseClosed,
independent_functionElimination,
productElimination,
axiomEquality,
universeEquality,
equalityElimination,
promote_hyp,
instantiate,
minusEquality
Latex:
\mforall{}[A:Type]. \mforall{}[f:A {}\mrightarrow{} wfd-tree(A)]. (mk-wfd-tree(f) \mmember{} wfd-tree(A))
Date html generated:
2018_05_21-PM-10_18_02
Last ObjectModification:
2017_07_26-PM-06_36_32
Theory : bar!induction
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