Nuprl Lemma : BNF-list-case0
∀ms:ℤ List. (imax-list([0 / ms]) ∈ ℕ)
Proof
Definitions occuring in Statement : 
imax-list: imax-list(L)
, 
cons: [a / b]
, 
list: T List
, 
nat: ℕ
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
natural_number: $n
, 
int: ℤ
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
nat: ℕ
, 
uall: ∀[x:A]. B[x]
, 
uimplies: b supposing a
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
rev_uimplies: rev_uimplies(P;Q)
, 
top: Top
, 
ge: i ≥ j 
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
le: A ≤ B
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
implies: P 
⇒ Q
, 
not: ¬A
, 
prop: ℙ
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
Lemmas referenced : 
list_wf, 
le_wf, 
l_member_wf, 
cons_member, 
member-le-max, 
int_formula_prop_wf, 
int_formula_prop_le_lemma, 
int_term_value_var_lemma, 
int_term_value_add_lemma, 
int_term_value_constant_lemma, 
int_formula_prop_less_lemma, 
int_formula_prop_not_lemma, 
int_formula_prop_and_lemma, 
intformle_wf, 
itermVar_wf, 
itermAdd_wf, 
itermConstant_wf, 
intformless_wf, 
intformnot_wf, 
intformand_wf, 
satisfiable-full-omega-tt, 
decidable__lt, 
non_neg_length, 
length_of_cons_lemma, 
cons_wf, 
length_wf, 
assert_of_lt_int, 
imax-list_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
cut, 
dependent_set_memberEquality, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
because_Cache, 
independent_isectElimination, 
natural_numberEquality, 
intEquality, 
hypothesisEquality, 
hypothesis, 
productElimination, 
sqequalRule, 
dependent_functionElimination, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
addEquality, 
unionElimination, 
dependent_pairFormation, 
lambdaEquality, 
int_eqEquality, 
independent_pairFormation, 
computeAll, 
independent_functionElimination, 
inlFormation
Latex:
\mforall{}ms:\mBbbZ{}  List.  (imax-list([0  /  ms])  \mmember{}  \mBbbN{})
Date html generated:
2016_05_16-AM-08_52_07
Last ObjectModification:
2016_01_17-AM-09_42_40
Theory : C-semantics
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