Nuprl Lemma : length-merge-int
∀[T:Type]. ∀[as,bs:T List]. (||merge-int(bs;as)|| = (||bs|| + ||as||) ∈ ℤ) supposing T ⊆r ℤ
Proof
Definitions occuring in Statement :
length: ||as||,
merge-int: merge-int(as;bs),
list: T List,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
add: n + m,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
merge-int: merge-int(as;bs),
all: ∀x:A. B[x],
top: Top,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
list_induction,
uall_wf,
list_wf,
equal_wf,
length_wf,
merge-int_wf,
reduce_nil_lemma,
length_of_nil_lemma,
add-zero,
reduce_cons_lemma,
length_of_cons_lemma,
squash_wf,
true_wf,
length-insert-int,
iff_weakening_equal,
add_functionality_wrt_eq,
general_add_assoc,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
cumulativity,
hypothesis,
intEquality,
independent_isectElimination,
addEquality,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
lambdaFormation,
rename,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeEquality,
productElimination,
axiomEquality
Latex:
\mforall{}[T:Type]. \mforall{}[as,bs:T List]. (||merge-int(bs;as)|| = (||bs|| + ||as||)) supposing T \msubseteq{}r \mBbbZ{}
Date html generated:
2017_04_14-AM-08_36_13
Last ObjectModification:
2017_02_27-PM-03_28_21
Theory : list_0
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