Nuprl Lemma : awf-example1_wf
awf-example1() ∈ awf-system{i:l}(ℕ3;ℤ)
Proof
Definitions occuring in Statement :
awf-example1: awf-example1(),
awf-system: awf-system{i:l}(I;A),
int_seg: {i..j-},
member: t ∈ T,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
awf-system: awf-system{i:l}(I;A),
awf-example1: awf-example1(),
member: t ∈ T,
isect2: T1 ⋂ T2,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
less_than: a < b,
squash: ↓T,
true: True,
uimplies: b supposing a,
guard: {T},
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s],
bfalse: ff
Lemmas referenced :
bool_wf,
top_wf,
awf_wf,
subtype_rel_wf,
set_wf,
int_seg_wf,
subtype_rel_union,
int_term_value_add_lemma,
int_formula_prop_less_lemma,
itermAdd_wf,
intformless_wf,
decidable__lt,
length_of_nil_lemma,
length_of_cons_lemma,
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,
int_seg_properties,
nil_wf,
lelt_wf,
false_wf,
awf-leaf_wf,
cons_wf,
list_wf,
select_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
isect_memberEquality,
sqequalHypSubstitution,
unionElimination,
thin,
equalityElimination,
lambdaEquality,
cut,
lemma_by_obid,
isectElimination,
unionEquality,
voidEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
because_Cache,
inrEquality,
intEquality,
natural_numberEquality,
applyEquality,
dependent_set_memberEquality,
independent_pairFormation,
lambdaFormation,
introduction,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
dependent_functionElimination,
dependent_pairFormation,
int_eqEquality,
voidElimination,
computeAll,
addEquality,
functionEquality,
instantiate,
universeEquality,
productEquality,
cumulativity,
functionExtensionality
Latex:
awf-example1() \mmember{} awf-system\{i:l\}(\mBbbN{}3;\mBbbZ{})
Date html generated:
2016_05_15-PM-07_27_23
Last ObjectModification:
2016_01_16-AM-09_41_26
Theory : general
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