Nuprl Lemma : sbdecode_wf
∀[L:ℕ2 List]. (sbdecode(L) ∈ ℕ+ × ℕ+)
Proof
Definitions occuring in Statement :
sbdecode: sbdecode(L),
list: T List,
int_seg: {i..j-},
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
member: t ∈ T,
product: x:A × B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
sbdecode: sbdecode(L),
int_seg: {i..j-},
nat_plus: ℕ+,
guard: {T},
lelt: i ≤ j < k,
and: P ∧ Q,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True
Lemmas referenced :
list_wf,
less_than_wf,
int_formula_prop_wf,
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,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__lt,
int_seg_properties,
nat_plus_properties,
nat_plus_wf,
int_seg_wf,
reduce_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
productEquality,
because_Cache,
lambdaEquality,
productElimination,
int_eqEquality,
setElimination,
rename,
hypothesisEquality,
independent_pairEquality,
dependent_set_memberEquality,
addEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
imageMemberEquality,
baseClosed,
axiomEquality
Latex:
\mforall{}[L:\mBbbN{}2 List]. (sbdecode(L) \mmember{} \mBbbN{}\msupplus{} \mtimes{} \mBbbN{}\msupplus{})
Date html generated:
2016_05_15-PM-10_34_14
Last ObjectModification:
2016_01_16-PM-09_37_41
Theory : rationals
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