Nuprl Lemma : finite-implies-finite'
∀[A:Type]. (finite(A) ⇒ finite'(A))
Proof
Definitions occuring in Statement :
finite: finite(T),
finite': finite'(T),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
finite: finite(T),
exists: ∃x:A. B[x],
member: t ∈ T,
nat: ℕ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
all: ∀x:A. B[x],
prop: ℙ
Lemmas referenced :
finite'_functionality_wrt_equipollent,
int_seg_wf,
nsub_finite',
finite_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
natural_numberEquality,
setElimination,
rename,
hypothesis,
independent_functionElimination,
dependent_functionElimination,
cumulativity,
universeEquality
Latex:
\mforall{}[A:Type]. (finite(A) {}\mRightarrow{} finite'(A))
Date html generated:
2016_10_21-AM-11_00_24
Last ObjectModification:
2016_08_06-PM-02_37_25
Theory : equipollence!!cardinality!
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