Nuprl Lemma : find-ge_wf
∀[n:ℤ]. ∀[f:{n...} ⟶ 𝔹]. find-ge(f;n) ∈ {n':ℤ| (n ≤ n') ∧ f n' = tt} supposing ∃m:{n...}. ∀k:{m...}. f k = tt
Proof
Definitions occuring in Statement :
find-ge: find-ge(f;n),
int_upper: {i...},
btrue: tt,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
and: P ∧ Q,
member: t ∈ T,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ⟶ B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
find-ge: find-ge(f;n),
int_upper: {i...},
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
and: P ∧ Q,
subtype_rel: A ⊆r B,
pi1: fst(t),
so_lambda: λ2x.t[x],
guard: {T},
so_apply: x[s]
Lemmas referenced :
int_formula_prop_and_lemma,
intformand_wf,
int_upper_properties,
int_upper_subtype_int_upper,
all_wf,
int_upper_wf,
exists_wf,
equal_wf,
int_subtype_base,
equal-wf-base,
or_wf,
bool_wf,
equal-wf-T-base,
less_than_wf,
le_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
itermVar_wf,
intformle_wf,
intformnot_wf,
satisfiable-full-omega-tt,
decidable__le,
find-xover_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
dependent_set_memberEquality,
hypothesisEquality,
productElimination,
dependent_functionElimination,
hypothesis,
unionElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
independent_pairFormation,
imageMemberEquality,
baseClosed,
productEquality,
setEquality,
applyEquality,
lambdaFormation,
setElimination,
rename,
baseApply,
closedConclusion,
addEquality,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
axiomEquality,
functionEquality
Latex:
\mforall{}[n:\mBbbZ{}]. \mforall{}[f:\{n...\} {}\mrightarrow{} \mBbbB{}]. find-ge(f;n) \mmember{} \{n':\mBbbZ{}| (n \mleq{} n') \mwedge{} f n' = tt\} supposing \mexists{}m:\{n...\}. \mforall{}k:\{m..\000C.\}. f k = tt
Date html generated:
2016_05_14-AM-07_28_30
Last ObjectModification:
2016_01_14-PM-09_59_03
Theory : int_2
Home
Index