Nuprl Lemma : lg-edge-map
∀[T,S:Type]. ∀f:T ⟶ S. ∀g:LabeledGraph(T). ∀a,b:ℕlg-size(g). (lg-edge(lg-map(f;g);a;b) ⇐⇒ lg-edge(g;a;b))
Proof
Definitions occuring in Statement :
lg-map: lg-map(f;g),
lg-edge: lg-edge(g;a;b),
lg-size: lg-size(g),
labeled-graph: LabeledGraph(T),
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
lg-edge: lg-edge(g;a;b),
lg-map: lg-map(f;g),
lg-size: lg-size(g),
lg-in-edges: lg-in-edges(g;x),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
subtype_rel: A ⊆r B,
labeled-graph: LabeledGraph(T),
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
nat: ℕ,
int_seg: {i..j-},
uimplies: b supposing a,
prop: ℙ,
ge: i ≥ j ,
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
spreadn: spread3,
pi2: snd(t),
pi1: fst(t),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}[T,S:Type].
\mforall{}f:T {}\mrightarrow{} S. \mforall{}g:LabeledGraph(T). \mforall{}a,b:\mBbbN{}lg-size(g). (lg-edge(lg-map(f;g);a;b) \mLeftarrow{}{}\mRightarrow{} lg-edge(g;a;b))
Date html generated:
2016_05_17-AM-10_12_22
Last ObjectModification:
2016_01_18-AM-00_22_02
Theory : process-model
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