Nuprl Lemma : lg-size-remove
∀[T:Type]. ∀[g:LabeledGraph(T)]. ∀[x:ℕlg-size(g)]. (lg-size(lg-remove(g;x)) = (lg-size(g) - 1) ∈ ℤ)
Proof
Definitions occuring in Statement :
lg-remove: lg-remove(g;n),
lg-size: lg-size(g),
labeled-graph: LabeledGraph(T),
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
subtract: n - m,
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
lg-size: lg-size(g),
lg-remove: lg-remove(g;n),
top: Top,
subtype_rel: A ⊆r B,
labeled-graph: LabeledGraph(T),
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
int_seg: {i..j-},
nat: ℕ,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
int_iseg: {i...j},
lelt: i ≤ j < k,
prop: ℙ,
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,
not: ¬A,
cand: A c∧ B,
true: True
Latex:
\mforall{}[T:Type]. \mforall{}[g:LabeledGraph(T)]. \mforall{}[x:\mBbbN{}lg-size(g)]. (lg-size(lg-remove(g;x)) = (lg-size(g) - 1))
Date html generated:
2016_05_17-AM-10_08_47
Last ObjectModification:
2016_01_18-AM-00_23_42
Theory : process-model
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