Nuprl Lemma : setTC-contains
∀a:Set{i:l}. (a ⊆ setTC(a))
Proof
Definitions occuring in Statement :
setsubset: (a ⊆ b),
setTC: setTC(a),
Set: Set{i:l},
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
setTC: Error :setTC,
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
or: P ∨ Q
Lemmas referenced :
setmem-set-add,
setunionfun_wf,
Set_wf,
setmem_wf,
setsubset-iff,
all_wf
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
sqequalRule,
lambdaEquality,
setElimination,
rename,
hypothesis,
setEquality,
cumulativity,
productElimination,
independent_functionElimination,
inlFormation,
because_Cache,
addLevel,
allFunctionality,
instantiate,
functionEquality
Latex:
\mforall{}a:Set\{i:l\}. (a \msubseteq{} setTC(a))
Date html generated:
2018_07_29-AM-10_03_35
Last ObjectModification:
2018_05_30-PM-00_30_40
Theory : constructive!set!theory
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