Nuprl Lemma : injectively-presented-singleset
∀a:Set{i:l}. InjectivelyPresented({a})
Proof
Definitions occuring in Statement :
injectively-presented: InjectivelyPresented(s),
singleset: {a},
Set: Set{i:l},
all: ∀x:A. B[x]
Definitions unfolded in proof :
prop: ℙ,
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
pi2: snd(t),
pi1: fst(t),
inject: Inj(A;B;f),
set-dom: set-dom(s),
set-item: set-item(s;x),
mkset: {f[t] | t ∈ T},
injectively-presented: InjectivelyPresented(s),
singleset: {a},
all: ∀x:A. B[x]
Lemmas referenced :
unit_wf2,
Set_wf,
member_wf,
equal-unit
Rules used in proof :
instantiate,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
sqequalRule,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}a:Set\{i:l\}. InjectivelyPresented(\{a\})
Date html generated:
2018_05_29-PM-01_55_17
Last ObjectModification:
2018_05_24-PM-10_10_59
Theory : constructive!set!theory
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