Nuprl Lemma : one-one_wf
∀[A,B:Type]. ∀[R:A ⟶ B ⟶ ℙ]. (one-one(A;B;R) ∈ ℙ)
Proof
Definitions occuring in Statement :
one-one: one-one(A;B;R),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
one-one: one-one(A;B;R),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
all_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
functionEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A,B:Type]. \mforall{}[R:A {}\mrightarrow{} B {}\mrightarrow{} \mBbbP{}]. (one-one(A;B;R) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-PM-03_55_54
Last ObjectModification:
2015_12_26-PM-06_55_25
Theory : relations2
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