Nuprl Lemma : testrec1_wf
∀[A:Type]. ∀[x:ℤ]. ∀[L:A List]. (testrec1(x;L) ∈ ℤ)
Proof
Definitions occuring in Statement :
testrec1: testrec1(x;L),
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
and: P ∧ Q,
prop: ℙ,
or: P ∨ Q,
testrec1: testrec1(x;L),
ifthenelse: if b then t else f fi ,
btrue: tt,
cons: [a / b],
le: A ≤ B,
less_than': less_than'(a;b),
colength: colength(L),
nil: [],
it: ⋅,
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
decidable: Dec(P),
subtype_rel: A ⊆r B,
bfalse: ff
Lemmas referenced :
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
istype-less_than,
list-cases,
null_nil_lemma,
reduce_tl_nil_lemma,
product_subtype_list,
colength-cons-not-zero,
colength_wf_list,
istype-void,
istype-le,
list_wf,
subtract-1-ge-0,
subtype_base_sq,
intformeq_wf,
int_formula_prop_eq_lemma,
set_subtype_base,
int_subtype_base,
spread_cons_lemma,
decidable__equal_int,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
itermAdd_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
int_term_value_add_lemma,
decidable__le,
le_wf,
null_cons_lemma,
reduce_tl_cons_lemma,
istype-nat,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
thin,
lambdaFormation_alt,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
dependent_functionElimination,
Error :memTop,
independent_pairFormation,
universeIsType,
voidElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionIsTypeImplies,
inhabitedIsType,
unionElimination,
promote_hyp,
hypothesis_subsumption,
productElimination,
equalityIstype,
because_Cache,
dependent_set_memberEquality_alt,
instantiate,
applyLambdaEquality,
imageElimination,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
intEquality,
sqequalBase,
multiplyEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[x:\mBbbZ{}]. \mforall{}[L:A List]. (testrec1(x;L) \mmember{} \mBbbZ{})
Date html generated:
2020_05_20-AM-08_20_28
Last ObjectModification:
2020_01_07-PM-04_08_02
Theory : general
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