### 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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