Nuprl Lemma : conjugate_wf
∀[n:ℕ]. ∀[f,g:ℕn →⟶ ℕn]. (conjugate(f;g) ∈ ℕn →⟶ ℕn)
Proof
Definitions occuring in Statement :
conjugate: conjugate(f;g),
injection: A →⟶ B,
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
conjugate: conjugate(f;g),
nat: ℕ
Lemmas referenced :
compose_wf-injection,
int_seg_wf,
funinv_wf3,
injection_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[f,g:\mBbbN{}n \mrightarrow{}{}\mrightarrow{} \mBbbN{}n]. (conjugate(f;g) \mmember{} \mBbbN{}n \mrightarrow{}{}\mrightarrow{} \mBbbN{}n)
Date html generated:
2016_05_15-PM-06_12_27
Last ObjectModification:
2015_12_27-PM-00_12_15
Theory : general
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