Nuprl Lemma : id_increasing
∀[k:ℕ]. increasing(λi.i;k)
Proof
Definitions occuring in Statement :
increasing: increasing(f;k),
nat: ℕ,
uall: ∀[x:A]. B[x],
lambda: λx.A[x]
Definitions unfolded in proof :
increasing: increasing(f;k),
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
int_seg: {i..j-},
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: 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,
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
true: True
Lemmas referenced :
decidable__lt,
false_wf,
not-lt-2,
condition-implies-le,
minus-add,
int_seg_wf,
subtract_wf,
minus-one-mul,
add-swap,
minus-one-mul-top,
add-mul-special,
zero-mul,
add-zero,
add-associates,
add-commutes,
le-add-cancel,
member-less_than,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
hypothesisEquality,
addEquality,
natural_numberEquality,
hypothesis,
unionElimination,
independent_pairFormation,
voidElimination,
productElimination,
independent_functionElimination,
independent_isectElimination,
isectElimination,
applyEquality,
lambdaEquality,
isect_memberEquality,
voidEquality,
intEquality,
minusEquality,
because_Cache,
multiplyEquality
Latex:
\mforall{}[k:\mBbbN{}]. increasing(\mlambda{}i.i;k)
Date html generated:
2016_05_13-PM-04_02_11
Last ObjectModification:
2015_12_26-AM-10_56_36
Theory : int_1
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