Nuprl Lemma : injection-bijection
∀n:ℕ. ∀f:ℕn →⟶ ℕn. Bij(ℕn;ℕn;f)
Proof
Definitions occuring in Statement :
injection: A →⟶ B,
biject: Bij(A;B;f),
int_seg: {i..j-},
nat: ℕ,
all: ∀x:A. B[x],
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
injection: A →⟶ B,
biject: Bij(A;B;f),
and: P ∧ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
uimplies: b supposing a
Lemmas referenced :
injection-is-surjection,
sq_stable__inject,
nat_wf,
int_seg_wf,
injection_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
independent_pairFormation,
hypothesis,
lemma_by_obid,
isectElimination,
natural_numberEquality,
hypothesisEquality,
independent_functionElimination,
introduction,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
dependent_functionElimination,
independent_isectElimination
Latex:
\mforall{}n:\mBbbN{}. \mforall{}f:\mBbbN{}n \mrightarrow{}{}\mrightarrow{} \mBbbN{}n. Bij(\mBbbN{}n;\mBbbN{}n;f)
Date html generated:
2016_05_15-PM-06_11_10
Last ObjectModification:
2016_01_16-PM-00_45_51
Theory : general
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