Nuprl Lemma : lg-remove-noop
∀[T:Type]. ∀[g:LabeledGraph(T)]. ∀[x:ℕ]. lg-remove(g;x) ~ g supposing lg-size(g) ≤ x
Proof
Definitions occuring in Statement :
lg-remove: lg-remove(g;n),
lg-size: lg-size(g),
labeled-graph: LabeledGraph(T),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
labeled-graph: LabeledGraph(T),
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
lg-size: lg-size(g),
nat: ℕ,
implies: P ⇒ Q,
uimplies: b supposing a,
prop: ℙ,
lg-remove: lg-remove(g;n),
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
and: P ∧ Q,
le: A ≤ B,
cons: [a / b],
colength: colength(L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
guard: {T},
nil: [],
it: ⋅,
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
spreadn: spread3,
int_seg: {i..j-},
bool: 𝔹,
unit: Unit,
btrue: tt,
uiff: uiff(P;Q),
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
bfalse: ff,
lelt: i ≤ j < k,
assert: ↑b,
nequal: a ≠ b ∈ T
Latex:
\mforall{}[T:Type]. \mforall{}[g:LabeledGraph(T)]. \mforall{}[x:\mBbbN{}]. lg-remove(g;x) \msim{} g supposing lg-size(g) \mleq{} x
Date html generated:
2016_05_17-AM-10_08_43
Last ObjectModification:
2016_01_18-AM-00_23_22
Theory : process-model
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