Nuprl Lemma : BNF-list-case1
∀ms:ℤ List. ∀n:ℕ.  (imax-list([0 / ms]) + n ∈ 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
, 
add: n + m
, 
natural_number: $n
, 
int: ℤ
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
nat: ℕ
, 
subtype_rel: A ⊆r B
, 
guard: {T}
, 
uall: ∀[x:A]. B[x]
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
ge: i ≥ j 
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
uimplies: b supposing a
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
not: ¬A
, 
top: Top
, 
and: P ∧ Q
Lemmas referenced : 
list_wf, 
int_formula_prop_wf, 
int_formula_prop_eq_lemma, 
int_term_value_add_lemma, 
int_term_value_var_lemma, 
int_term_value_constant_lemma, 
int_formula_prop_le_lemma, 
int_formula_prop_not_lemma, 
int_formula_prop_and_lemma, 
intformeq_wf, 
itermAdd_wf, 
itermVar_wf, 
itermConstant_wf, 
intformle_wf, 
intformnot_wf, 
intformand_wf, 
satisfiable-full-omega-tt, 
decidable__le, 
le_wf, 
nat_properties, 
add_nat_wf, 
nat_wf, 
BNF-list-case0
Rules used in proof : 
cut, 
lemma_by_obid, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
hypothesis, 
sqequalHypSubstitution, 
dependent_functionElimination, 
thin, 
hypothesisEquality, 
dependent_set_memberEquality, 
addEquality, 
equalityTransitivity, 
equalitySymmetry, 
applyEquality, 
lambdaEquality, 
setElimination, 
rename, 
sqequalRule, 
isectElimination, 
setEquality, 
intEquality, 
natural_numberEquality, 
unionElimination, 
independent_isectElimination, 
dependent_pairFormation, 
int_eqEquality, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
independent_pairFormation, 
computeAll, 
equalityEquality, 
independent_functionElimination
Latex:
\mforall{}ms:\mBbbZ{}  List.  \mforall{}n:\mBbbN{}.    (imax-list([0  /  ms])  +  n  \mmember{}  \mBbbN{})
Date html generated:
2016_05_16-AM-08_52_11
Last ObjectModification:
2016_01_17-AM-09_42_05
Theory : C-semantics
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