Nuprl Lemma : is-dag-add
∀[T:Type]. ∀[g:LabeledGraph(T)]. ∀[y:ℕlg-size(g)]. ∀[x:ℕy]. is-dag(lg-add(g;x;y)) supposing is-dag(g)
Proof
Definitions occuring in Statement :
is-dag: is-dag(g),
lg-add: lg-add(g;a;b),
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,
is-dag: is-dag(g),
all: ∀x:A. B[x],
implies: P ⇒ Q,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than: a < b,
prop: ℙ,
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
iff: P ⇐⇒ Q,
subtype_rel: A ⊆r B,
squash: ↓T
Latex:
\mforall{}[T:Type]. \mforall{}[g:LabeledGraph(T)]. \mforall{}[y:\mBbbN{}lg-size(g)]. \mforall{}[x:\mBbbN{}y].
is-dag(lg-add(g;x;y)) supposing is-dag(g)
Date html generated:
2016_05_17-AM-10_11_34
Last ObjectModification:
2016_01_18-AM-00_22_16
Theory : process-model
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