Nuprl Lemma : has-value-mklist
∀[n,f:Base]. n ∈ ℤ supposing (mklist(n;f))↓
Proof
Definitions occuring in Statement :
mklist: mklist(n;f),
has-value: (a)↓,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ,
base: Base
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
mklist: mklist(n;f),
top: Top,
prop: ℙ,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
and: P ∧ Q,
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
nat_plus: ℕ+,
has-value: (a)↓
Lemmas referenced :
primrec-as-fix,
has-value_wf_base,
base_wf,
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
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,
less_than_wf,
int_subtype_base,
fun_exp0_lemma,
strictness-apply,
bottom_diverge,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
fun_exp_unroll_1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
sqequalRule,
extract_by_obid,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
because_Cache,
compactness,
setElimination,
rename,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
independent_pairFormation,
applyEquality,
unionElimination,
dependent_set_memberEquality,
callbyvalueLess,
productElimination
Latex:
\mforall{}[n,f:Base]. n \mmember{} \mBbbZ{} supposing (mklist(n;f))\mdownarrow{}
Date html generated:
2018_05_21-PM-00_37_58
Last ObjectModification:
2018_05_19-AM-06_44_17
Theory : list_1
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