Nuprl Lemma : injectively-presented-presentable
∀a:Set{i:l}. (InjectivelyPresented(a) ⇒ InjectivelyPresentable(a))
Proof
Definitions occuring in Statement :
injectively-presentable: InjectivelyPresentable(a),
injectively-presented: InjectivelyPresented(s),
Set: Set{i:l},
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
prop: ℙ,
cand: A c∧ B,
and: P ∧ Q,
member: t ∈ T,
exists: ∃x:A. B[x],
injectively-presentable: InjectivelyPresentable(a),
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
Set_wf,
seteq_wf,
injectively-presented_wf,
seteq_weakening
Rules used in proof :
cumulativity,
isectElimination,
productEquality,
independent_functionElimination,
because_Cache,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
independent_pairFormation,
hypothesis,
cut,
hypothesisEquality,
dependent_pairFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}a:Set\{i:l\}. (InjectivelyPresented(a) {}\mRightarrow{} InjectivelyPresentable(a))
Date html generated:
2018_05_29-PM-01_55_26
Last ObjectModification:
2018_05_24-PM-10_15_37
Theory : constructive!set!theory
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