Nuprl Lemma : lg-contains_antisymmetry
∀[T:Type]. ∀[g1,g2:LabeledGraph(T)]. (g1 = g2 ∈ LabeledGraph(T)) supposing (g2 ⊆ g1 and g1 ⊆ g2)
Proof
Definitions occuring in Statement :
lg-contains: g1 ⊆ g2,
labeled-graph: LabeledGraph(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
lg-contains: g1 ⊆ g2,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
nat: ℕ,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
guard: {T},
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
iff: P ⇐⇒ Q,
uiff: uiff(P;Q),
squash: ↓T,
true: True,
rev_implies: P ⇐ Q
Latex:
\mforall{}[T:Type]. \mforall{}[g1,g2:LabeledGraph(T)]. (g1 = g2) supposing (g2 \msubseteq{} g1 and g1 \msubseteq{} g2)
Date html generated:
2016_05_17-AM-10_08_57
Last ObjectModification:
2016_01_18-AM-00_22_55
Theory : process-model
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