Nuprl Lemma : increasing_wf
∀[k:ℕ]. ∀[f:ℕk ⟶ ℤ]. (increasing(f;k) ∈ ℙ)
Proof
Definitions occuring in Statement :
increasing: increasing(f;k),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
increasing: increasing(f;k),
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
false: False,
prop: ℙ,
uiff: uiff(P;Q),
uimplies: b supposing a,
subtract: n - m,
subtype_rel: A ⊆r B,
top: Top,
less_than': less_than'(a;b),
true: True,
so_apply: x[s]
Lemmas referenced :
all_wf,
int_seg_wf,
subtract_wf,
less_than_wf,
decidable__lt,
false_wf,
not-lt-2,
less-iff-le,
condition-implies-le,
add-associates,
nat_wf,
minus-add,
minus-one-mul,
add-swap,
minus-one-mul-top,
add-commutes,
add_functionality_wrt_le,
le-add-cancel2,
lelt_wf,
add-member-int_seg2,
decidable__le,
not-le-2,
zero-add,
add-zero
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
lambdaEquality,
applyEquality,
dependent_set_memberEquality,
productElimination,
independent_pairFormation,
dependent_functionElimination,
unionElimination,
lambdaFormation,
voidElimination,
independent_functionElimination,
independent_isectElimination,
addEquality,
minusEquality,
isect_memberEquality,
voidEquality,
intEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[f:\mBbbN{}k {}\mrightarrow{} \mBbbZ{}]. (increasing(f;k) \mmember{} \mBbbP{})
Date html generated:
2016_05_13-PM-04_02_10
Last ObjectModification:
2015_12_26-AM-10_56_53
Theory : int_1
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