Nuprl Lemma : insert-no-combine-permutation

`∀T:Type. ∀cmp:comparison(T). ∀L:T List. ∀u:T.  permutation(T;insert-no-combine(cmp;u;L);[u] @ L)`

Proof

Definitions occuring in Statement :  insert-no-combine: `insert-no-combine(cmp;x;l)` comparison: `comparison(T)` permutation: `permutation(T;L1;L2)` append: `as @ bs` cons: `[a / b]` nil: `[]` list: `T List` all: `∀x:A. B[x]` universe: `Type`
Definitions unfolded in proof :  all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` member: `t ∈ T` so_lambda: `λ2x.t[x]` so_apply: `x[s]` implies: `P `` Q` insert-no-combine: `insert-no-combine(cmp;x;l)` so_lambda: `so_lambda(x,y,z.t[x; y; z])` top: `Top` so_apply: `x[s1;s2;s3]` append: `as @ bs` uimplies: `b supposing a` comparison: `comparison(T)` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` and: `P ∧ Q` ifthenelse: `if b then t else f fi ` bfalse: `ff` exists: `∃x:A. B[x]` prop: `ℙ` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` false: `False` not: `¬A` iff: `P `⇐⇒` Q` rev_implies: `P `` Q`
Lemmas referenced :  list_induction all_wf permutation_wf insert-no-combine_wf append_wf cons_wf nil_wf list_wf list_ind_nil_lemma list_ind_cons_lemma permutation_weakening le_int_wf bool_wf eqtt_to_assert assert_of_le_int eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot le_wf comparison_wf permutation_functionality_wrt_permutation cons_functionality_wrt_permutation permutation-swap-first2
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut thin introduction extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality sqequalRule lambdaEquality cumulativity hypothesis independent_functionElimination dependent_functionElimination isect_memberEquality voidElimination voidEquality because_Cache independent_isectElimination rename natural_numberEquality applyEquality setElimination unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination dependent_pairFormation promote_hyp instantiate universeEquality

Latex:
\mforall{}T:Type.  \mforall{}cmp:comparison(T).  \mforall{}L:T  List.  \mforall{}u:T.    permutation(T;insert-no-combine(cmp;u;L);[u]  @  L)

Date html generated: 2017_04_17-AM-08_30_42
Last ObjectModification: 2017_02_27-PM-04_52_15

Theory : list_1

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