Nuprl Lemma : graph-cosets_wf
∀[I:Type]. ∀[E:I ⟶ I ⟶ ℙ]. (graph-cosets(I;i,j.E[i;j]) ∈ I ⟶ coSet{i:l})
Proof
Definitions occuring in Statement :
graph-cosets: graph-cosets(I;i,j.E[i; j]),
coSet: coSet{i:l},
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
graph-cosets: graph-cosets(I;i,j.E[i; j]),
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
fix_wf_coSet_system_weak,
subtype_rel_self,
pi1_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
isect_memberEquality,
lambdaEquality,
dependent_pairEquality,
productEquality,
applyEquality,
hypothesis,
sqequalRule,
instantiate,
because_Cache,
functionEquality,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[I:Type]. \mforall{}[E:I {}\mrightarrow{} I {}\mrightarrow{} \mBbbP{}]. (graph-cosets(I;i,j.E[i;j]) \mmember{} I {}\mrightarrow{} coSet\{i:l\})
Date html generated:
2019_10_31-AM-06_33_03
Last ObjectModification:
2018_08_08-AM-08_17_18
Theory : constructive!set!theory
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