Nuprl Lemma : equiv-equipollent_wf
∀[A,B:Type]. ∀[E:A ⟶ A ⟶ ℙ]. (A ~ B mod (a1,a2.E[a1;a2]) ∈ ℙ)
Proof
Definitions occuring in Statement :
equiv-equipollent: A ~ B mod (a1,a2.E[a1; a2]),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
equiv-equipollent: A ~ B mod (a1,a2.E[a1; a2]),
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s1;s2],
so_apply: x[s],
iff: P ⇐⇒ Q,
all: ∀x:A. B[x],
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
exists_wf,
surject_wf,
all_wf,
iff_wf,
equal_wf,
squash_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesisEquality,
lambdaEquality,
productEquality,
hypothesis,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A,B:Type]. \mforall{}[E:A {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{}]. (A \msim{} B mod (a1,a2.E[a1;a2]) \mmember{} \mBbbP{})
Date html generated:
2018_05_21-PM-00_52_57
Last ObjectModification:
2018_05_19-AM-06_39_40
Theory : equipollence!!cardinality!
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