Nuprl Lemma : no_repeats-permutations-list
∀n:ℕ. no_repeats(ℕn →⟶ ℕn;permutations-list(n))
Proof
Definitions occuring in Statement :
permutations-list: permutations-list(n),
injection: A →⟶ B,
no_repeats: no_repeats(T;l),
int_seg: {i..j-},
nat: ℕ,
all: ∀x:A. B[x],
natural_number: $n
Definitions unfolded in proof :
squash: ↓T,
sq_stable: SqStable(P),
implies: P ⇒ Q,
so_apply: x[s],
prop: ℙ,
and: P ∧ Q,
so_lambda: λ2x.t[x],
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
nat_wf,
equal_wf,
sq_stable__no_repeats,
l_member_wf,
all_wf,
no_repeats_wf,
int_seg_wf,
injection_wf,
list_wf,
set_wf,
permutations-list_wf
Rules used in proof :
dependent_functionElimination,
equalitySymmetry,
equalityTransitivity,
imageElimination,
baseClosed,
imageMemberEquality,
productElimination,
independent_functionElimination,
productEquality,
lambdaEquality,
sqequalRule,
because_Cache,
rename,
setElimination,
natural_numberEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}n:\mBbbN{}. no\_repeats(\mBbbN{}n \mrightarrow{}{}\mrightarrow{} \mBbbN{}n;permutations-list(n))
Date html generated:
2018_05_21-PM-08_22_15
Last ObjectModification:
2017_12_15-PM-00_17_45
Theory : general
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