Nuprl Lemma : cosetTC-set-function
∀s:coSet{i:l}. set-function{i:l}(s; a.cosetTC(a))
Proof
Definitions occuring in Statement :
cosetTC: cosetTC(a),
set-function: set-function{i:l}(s; x.f[x]),
coSet: coSet{i:l},
all: ∀x:A. B[x]
Definitions unfolded in proof :
prop: ℙ,
nat: ℕ,
subtype_rel: A ⊆r B,
coSet: coSet{i:l},
so_apply: x[s],
so_lambda: λ2x.t[x],
cosetTC: cosetTC(a),
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
set-function: set-function{i:l}(s; x.f[x]),
all: ∀x:A. B[x]
Lemmas referenced :
setmem_wf,
seteq_wf,
coSet_wf,
subtype_rel_self,
copath-at_wf,
nat_wf,
copath-length_wf,
less_than_wf,
copath_wf,
mk-coset_wf,
seteq_weakening,
cosetTC_functionality,
cosetTC_wf,
seteq_functionality
Rules used in proof :
instantiate,
rename,
setElimination,
applyEquality,
natural_numberEquality,
lambdaEquality,
universeEquality,
setEquality,
sqequalRule,
productElimination,
independent_functionElimination,
because_Cache,
hypothesis,
hypothesisEquality,
isectElimination,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}s:coSet\{i:l\}. set-function\{i:l\}(s; a.cosetTC(a))
Date html generated:
2018_07_29-AM-10_01_44
Last ObjectModification:
2018_07_18-PM-06_41_04
Theory : constructive!set!theory
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