Nuprl Lemma : member-permutations-list
∀n:ℕ. ∀f:ℕn →⟶ ℕn. (f ∈ permutations-list(n))
Proof
Definitions occuring in Statement :
permutations-list: permutations-list(n),
injection: A →⟶ B,
l_member: (x ∈ l),
int_seg: {i..j-},
nat: ℕ,
all: ∀x:A. B[x],
natural_number: $n
Definitions unfolded in proof :
guard: {T},
false: False,
or: P ∨ Q,
decidable: Dec(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],
not: ¬A
Lemmas referenced :
nat_wf,
equal_wf,
decidable__equal_int_seg,
decidable__equal_injection,
decidable__l_member,
l_member_wf,
all_wf,
no_repeats_wf,
int_seg_wf,
injection_wf,
list_wf,
set_wf,
permutations-list_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
voidElimination,
unionElimination,
productElimination,
independent_functionElimination,
dependent_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{}. \mforall{}f:\mBbbN{}n \mrightarrow{}{}\mrightarrow{} \mBbbN{}n. (f \mmember{} permutations-list(n))
Date html generated:
2018_05_21-PM-08_22_03
Last ObjectModification:
2017_12_15-PM-00_03_02
Theory : general
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