Nuprl Lemma : lg-acyclic-remove
∀[T:Type]. ∀[g:LabeledGraph(T)]. ∀[i:ℕlg-size(g)]. lg-acyclic(lg-remove(g;i)) supposing lg-acyclic(g)
Proof
Definitions occuring in Statement :
lg-acyclic: lg-acyclic(g),
lg-remove: lg-remove(g;n),
lg-size: lg-size(g),
labeled-graph: LabeledGraph(T),
int_seg: {i..j-},
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
lg-acyclic: lg-acyclic(g),
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
sq_type: SQType(T),
int_seg: {i..j-},
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
lelt: i ≤ j < k,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
prop: ℙ,
le: A ≤ B,
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
subtract: n - m,
less_than': less_than'(a;b)
Latex:
\mforall{}[T:Type]. \mforall{}[g:LabeledGraph(T)].
\mforall{}[i:\mBbbN{}lg-size(g)]. lg-acyclic(lg-remove(g;i)) supposing lg-acyclic(g)
Date html generated:
2016_05_17-AM-10_10_28
Last ObjectModification:
2016_01_18-AM-00_22_24
Theory : process-model
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