Nuprl Lemma : equipollent-general-subtract-one
∀a:ℕ. ∀[T:Type]. (T ~ ℕa ⇒ (∀i:T. {x:T| ¬(x = i ∈ T)} ~ ℕa - 1))
Proof
Definitions occuring in Statement :
equipollent: A ~ B,
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
set: {x:A| B[x]} ,
subtract: n - m,
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
equipollent-subtract2,
false_wf,
le_wf,
equal_wf,
equipollent-one,
equipollent_wf,
int_seg_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
hypothesis,
isectElimination,
because_Cache,
independent_functionElimination,
lambdaEquality,
setElimination,
rename,
universeEquality
Latex:
\mforall{}a:\mBbbN{}. \mforall{}[T:Type]. (T \msim{} \mBbbN{}a {}\mRightarrow{} (\mforall{}i:T. \{x:T| \mneg{}(x = i)\} \msim{} \mBbbN{}a - 1))
Date html generated:
2016_05_14-PM-04_03_41
Last ObjectModification:
2015_12_26-PM-07_42_18
Theory : equipollence!!cardinality!
Home
Index