Nuprl Lemma : setmem-coset
∀T:Type. ∀f:T ⟶ coSet{i:l}. ∀t:T. (f t ∈ mk-coset(T;f))
Proof
Definitions occuring in Statement :
setmem: (x ∈ s),
mk-coset: mk-coset(T;f),
coSet: coSet{i:l},
all: ∀x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
prop: ℙ,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
top: Top,
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
coSet_wf,
seteq_wf,
seteq_weakening,
setmem-mk-coset
Rules used in proof :
universeEquality,
cumulativity,
functionEquality,
independent_functionElimination,
because_Cache,
applyEquality,
dependent_functionElimination,
hypothesisEquality,
dependent_pairFormation,
hypothesis,
voidEquality,
voidElimination,
isect_memberEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}T:Type. \mforall{}f:T {}\mrightarrow{} coSet\{i:l\}. \mforall{}t:T. (f t \mmember{} mk-coset(T;f))
Date html generated:
2018_07_29-AM-09_52_00
Last ObjectModification:
2018_07_20-PM-06_07_35
Theory : constructive!set!theory
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