Nuprl Lemma : const_nondecreasing
∀[k:ℕ]. ∀[x:ℤ]. nondecreasing(λi.x;k)
Proof
Definitions occuring in Statement :
nondecreasing: nondecreasing(f;k),
nat: ℕ,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
int: ℤ
Definitions unfolded in proof :
nondecreasing: nondecreasing(f;k),
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
guard: {T},
nat: ℕ,
int_seg: {i..j-},
ge: i ≥ j ,
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
prop: ℙ,
le: A ≤ B
Lemmas referenced :
int_seg_properties,
subtract_wf,
nat_properties,
decidable__le,
full-omega-unsat,
intformnot_wf,
intformle_wf,
itermVar_wf,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
int_seg_wf,
less_than'_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
productElimination,
dependent_functionElimination,
because_Cache,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairEquality,
axiomEquality
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[x:\mBbbZ{}]. nondecreasing(\mlambda{}i.x;k)
Date html generated:
2018_05_21-PM-01_00_01
Last ObjectModification:
2018_05_19-AM-06_36_25
Theory : num_thy_1
Home
Index