Nuprl Lemma : id-graph-edge_wf
∀[S:Id List]. ∀[G:Graph(S)]. ∀[i:{i:Id| (i ∈ S)} ]. ∀[j:Id]. ((i⟶j)∈G ∈ ℙ)
Proof
Definitions occuring in Statement :
id-graph-edge: (i⟶j)∈G,
id-graph: Graph(S),
Id: Id,
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
set: {x:A| B[x]}
Definitions unfolded in proof :
id-graph-edge: (i⟶j)∈G,
uall: ∀[x:A]. B[x],
member: t ∈ T,
id-graph: Graph(S),
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
l_member_wf,
Id_wf,
subtype_rel_list,
set_wf,
id-graph_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
applyEquality,
setEquality,
independent_isectElimination,
lambdaEquality,
setElimination,
rename,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[S:Id List]. \mforall{}[G:Graph(S)]. \mforall{}[i:\{i:Id| (i \mmember{} S)\} ]. \mforall{}[j:Id]. ((i{}\mrightarrow{}j)\mmember{}G \mmember{} \mBbbP{})
Date html generated:
2016_05_14-PM-03_37_45
Last ObjectModification:
2015_12_26-PM-05_58_56
Theory : decidable!equality
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