Nuprl Lemma : equipollent-one
∀[A:Type]. ∀a:A. {x:A| x = a ∈ A} ~ ℕ1
Proof
Definitions occuring in Statement :
equipollent: A ~ B,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
set: {x:A| B[x]} ,
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
prop: ℙ,
member: t ∈ T,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x]
Lemmas referenced :
all_wf,
set_wf,
equal_wf,
equipollent-one-iff
Rules used in proof :
universeEquality,
lambdaEquality,
sqequalRule,
because_Cache,
levelHypothesis,
addLevel,
rename,
setElimination,
dependent_set_memberEquality,
dependent_pairFormation,
independent_functionElimination,
productElimination,
hypothesis,
hypothesisEquality,
cumulativity,
setEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[A:Type]. \mforall{}a:A. \{x:A| x = a\} \msim{} \mBbbN{}1
Date html generated:
2018_05_21-PM-00_52_48
Last ObjectModification:
2017_12_07-PM-06_29_40
Theory : equipollence!!cardinality!
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