Nuprl Lemma : cosetTC_wf2
∀[a:Set{i:l}]. (cosetTC(a) ∈ Set{i:l})
Proof
Definitions occuring in Statement :
cosetTC: cosetTC(a),
Set: Set{i:l},
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
guard: {T},
prop: ℙ,
nat: ℕ,
so_apply: x[s],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
member: t ∈ T,
Set: Set{i:l},
Wsup: Wsup(a;b),
mk-coset: mk-coset(T;f),
cosetTC: cosetTC(a),
uall: ∀[x:A]. B[x]
Lemmas referenced :
Set_wf,
nat_wf,
copath-length_wf,
less_than_wf,
copath_wf,
Wsup_wf,
copath-at-W,
W-subtype-coW
Rules used in proof :
because_Cache,
rename,
setElimination,
natural_numberEquality,
setEquality,
cumulativity,
instantiate,
hypothesis,
lambdaEquality,
sqequalRule,
universeEquality,
isectElimination,
extract_by_obid,
introduction,
thin,
applyEquality,
hypothesisEquality,
cut,
sqequalHypSubstitution,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[a:Set\{i:l\}]. (cosetTC(a) \mmember{} Set\{i:l\})
Date html generated:
2018_07_29-AM-10_00_23
Last ObjectModification:
2018_07_19-AM-10_24_03
Theory : constructive!set!theory
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