Nuprl Lemma : lg-label-remove
∀[T:Type]. ∀[g:LabeledGraph(T)]. ∀[k:ℕlg-size(g)]. ∀[x:ℕlg-size(g) - 1].
(lg-label(lg-remove(g;k);x) ~ if x <z k then lg-label(g;x) else lg-label(g;x + 1) fi )
Proof
Definitions occuring in Statement :
lg-label: lg-label(g;x),
lg-remove: lg-remove(g;n),
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,
add: 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],
lg-label: lg-label(g;x),
lg-remove: lg-remove(g;n),
subtype_rel: A ⊆r B,
nat: ℕ,
top: Top,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than: a < b,
guard: {T},
prop: ℙ,
uimplies: b supposing a,
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
int_iseg: {i...j},
so_lambda: λ2x.t[x],
so_apply: x[s],
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,
false: False,
not: ¬A,
less_than': less_than'(a;b),
spreadn: spread3,
pi1: fst(t),
ge: i ≥ j ,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla)
Latex:
\mforall{}[T:Type]. \mforall{}[g:LabeledGraph(T)]. \mforall{}[k:\mBbbN{}lg-size(g)]. \mforall{}[x:\mBbbN{}lg-size(g) - 1].
(lg-label(lg-remove(g;k);x) \msim{} if x <z k then lg-label(g;x) else lg-label(g;x + 1) fi )
Date html generated:
2016_05_17-AM-10_17_54
Last ObjectModification:
2016_01_18-AM-00_22_21
Theory : process-model
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