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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