Nuprl Lemma : lg-label-map
∀[f:Top]. ∀[g:LabeledGraph(Top)]. ∀[x:ℕlg-size(g)]. (lg-label(lg-map(f;g);x) ~ f lg-label(g;x))
Proof
Definitions occuring in Statement :
lg-map: lg-map(f;g),
lg-label: lg-label(g;x),
lg-size: lg-size(g),
labeled-graph: LabeledGraph(T),
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
labeled-graph: LabeledGraph(T),
lg-size: lg-size(g),
subtype_rel: A ⊆r B,
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
lg-label: lg-label(g;x),
lg-map: lg-map(f;g),
guard: {T},
int_seg: {i..j-},
prop: ℙ,
ge: i ≥ j ,
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
select: L[n],
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
cons: [a / b],
colength: colength(L),
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
spreadn: spread3,
bool: 𝔹,
unit: Unit,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
pi1: fst(t),
bfalse: ff,
bnot: ¬bb,
assert: ↑b
Latex:
\mforall{}[f:Top]. \mforall{}[g:LabeledGraph(Top)]. \mforall{}[x:\mBbbN{}lg-size(g)]. (lg-label(lg-map(f;g);x) \msim{} f lg-label(g;x))
Date html generated:
2016_05_17-AM-10_12_43
Last ObjectModification:
2016_01_18-AM-00_21_50
Theory : process-model
Home
Index