Nuprl Lemma : permutation-length
∀[A:Type]. ∀[L1,L2:A List]. ||L1|| = ||L2|| ∈ ℤ supposing permutation(A;L1;L2)
Proof
Definitions occuring in Statement :
permutation: permutation(T;L1;L2),
length: ||as||,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
permutation: permutation(T;L1;L2),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
exists: ∃x:A. B[x],
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
top: Top
Lemmas referenced :
exists_wf,
int_seg_wf,
length_wf,
inject_wf,
equal_wf,
list_wf,
permute_list_wf,
permute_list_length
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis,
extract_by_obid,
isectElimination,
functionEquality,
natural_numberEquality,
hypothesisEquality,
lambdaEquality,
productEquality,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
voidElimination,
voidEquality,
hyp_replacement,
applyLambdaEquality,
intEquality
Latex:
\mforall{}[A:Type]. \mforall{}[L1,L2:A List]. ||L1|| = ||L2|| supposing permutation(A;L1;L2)
Date html generated:
2019_06_20-PM-01_37_21
Last ObjectModification:
2018_08_16-PM-01_17_07
Theory : list_1
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