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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