Nuprl Lemma : lg-label-append
∀[T:Type]. ∀[g1,g2:LabeledGraph(T)]. ∀[x:ℕlg-size(lg-append(g1;g2))].
(lg-label(lg-append(g1;g2);x) ~ if x <z lg-size(g1) then lg-label(g1;x) else lg-label(g2;x - lg-size(g1)) fi )
Proof
Definitions occuring in Statement :
lg-label: lg-label(g;x),
lg-append: lg-append(g1;g2),
lg-size: lg-size(g),
labeled-graph: LabeledGraph(T),
int_seg: {i..j-},
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
uall: ∀[x:A]. B[x],
subtract: n - m,
natural_number: $n,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
labeled-graph: LabeledGraph(T),
member: t ∈ T,
lg-size: lg-size(g),
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
nat: ℕ,
lg-label: lg-label(g;x),
lg-append: lg-append(g1;g2),
guard: {T},
spreadn: spread3,
int_seg: {i..j-},
uimplies: b supposing a,
top: Top,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
ge: i ≥ j ,
lelt: i ≤ j < k,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
pi1: fst(t)
Latex:
\mforall{}[T:Type]. \mforall{}[g1,g2:LabeledGraph(T)]. \mforall{}[x:\mBbbN{}lg-size(lg-append(g1;g2))].
(lg-label(lg-append(g1;g2);x) \msim{} if x <z lg-size(g1)
then lg-label(g1;x)
else lg-label(g2;x - lg-size(g1))
fi )
Date html generated:
2016_05_17-AM-10_12_49
Last ObjectModification:
2016_01_18-AM-00_21_18
Theory : process-model
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