Nuprl Lemma : no_repeats-residues-mod
∀[n:ℕ]. no_repeats(residue(n);residues-mod(n))
Proof
Definitions occuring in Statement :
residues-mod: residues-mod(n),
residue: residue(n),
no_repeats: no_repeats(T;l),
nat: ℕ,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
residues-mod: residues-mod(n),
nat: ℕ,
subtype_rel: A ⊆r B,
int_seg: {i..j-},
and: P ∧ Q
Lemmas referenced :
no_repeats-subtype,
residues-mod_wf,
no_repeats_witness,
residue_wf,
nat_wf,
no_repeats_filter,
eq_int_wf,
gcd_wf,
upto_wf,
subtype_rel_list,
int_seg_wf,
no_repeats_upto
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
independent_isectElimination,
hypothesis,
hypothesisEquality,
dependent_functionElimination,
independent_functionElimination,
intEquality,
lambdaEquality,
setElimination,
rename,
natural_numberEquality,
applyEquality,
sqequalRule,
productElimination
Latex:
\mforall{}[n:\mBbbN{}]. no\_repeats(residue(n);residues-mod(n))
Date html generated:
2016_05_15-PM-07_31_05
Last ObjectModification:
2015_12_27-AM-11_19_20
Theory : general
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