Nuprl Lemma : imax-list-append
∀[as,bs:ℤ List]. imax-list(as @ bs) = imax-list(bs @ as) ∈ ℤ supposing 0 < ||as @ bs||
Proof
Definitions occuring in Statement :
imax-list: imax-list(L),
length: ||as||,
append: as @ bs,
list: T List,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
imax-list: imax-list(L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
assoc: Assoc(T;op),
infix_ap: x f y,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
comm: Comm(T;op)
Lemmas referenced :
combine-list-append,
imax_wf,
equal_wf,
squash_wf,
true_wf,
imax_assoc,
iff_weakening_equal,
imax_com,
less_than_wf,
length_wf,
append_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
sqequalRule,
lambdaEquality,
hypothesisEquality,
hypothesis,
independent_isectElimination,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
because_Cache,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[as,bs:\mBbbZ{} List]. imax-list(as @ bs) = imax-list(bs @ as) supposing 0 < ||as @ bs||
Date html generated:
2017_04_17-AM-07_39_31
Last ObjectModification:
2017_02_27-PM-04_12_46
Theory : list_1
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