Nuprl Lemma : setTC-set-function
∀s:Set{i:l}. set-function{i:l}(s; a.setTC(a))
Proof
Definitions occuring in Statement :
setTC: setTC(a),
set-function: set-function{i:l}(s; x.f[x]),
Set: Set{i:l},
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
set-function: set-function{i:l}(s; x.f[x]),
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
seteq_wf,
setmem_wf,
Set_wf,
setTC_wf,
seteq_weakening,
seteq_functionality,
setTC_functionality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
because_Cache,
dependent_functionElimination,
independent_functionElimination,
productElimination
Latex:
\mforall{}s:Set\{i:l\}. set-function\{i:l\}(s; a.setTC(a))
Date html generated:
2018_05_22-PM-09_51_25
Last ObjectModification:
2018_05_22-AM-10_57_01
Theory : constructive!set!theory
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