Nuprl Lemma : has-value-l-last-default-list
∀[l,d:Base]. l ∈ Top List supposing (l-last-default(l;d))↓
Proof
Definitions occuring in Statement :
l-last-default: l-last-default(l;d),
list: T List,
has-value: (a)↓,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
base: Base
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
l-last-default: l-last-default(l;d),
list_ind: list_ind,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
nat_plus: ℕ+,
has-value: (a)↓,
cons: [a / b],
guard: {T},
it: ⋅,
nil: []
Lemmas referenced :
nil_wf,
has-value-implies-dec-isaxiom-2,
cons_wf,
top_wf,
has-value-implies-dec-ispair-2,
fun_exp_unroll_1,
int_term_value_subtract_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
intformnot_wf,
subtract_wf,
decidable__le,
bottom_diverge,
strictness-apply,
fun_exp0_lemma,
base_wf,
int_subtype_base,
has-value_wf_base,
less_than_wf,
ge_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
sqequalRule,
hypothesis,
compactness,
thin,
lemma_by_obid,
isectElimination,
hypothesisEquality,
setElimination,
rename,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
unionElimination,
dependent_set_memberEquality,
callbyvalueApply,
callbyvalueCallbyvalue,
callbyvalueReduce,
because_Cache
Latex:
\mforall{}[l,d:Base]. l \mmember{} Top List supposing (l-last-default(l;d))\mdownarrow{}
Date html generated:
2016_05_14-AM-07_41_42
Last ObjectModification:
2016_01_15-AM-08_36_29
Theory : list_1
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