`∀[T:Type]. ∀L:T List. ∀x,y:T.  (adjacent(T;rev(L);x;y) `⇐⇒` adjacent(T;L;y;x))`

Proof

Definitions occuring in Statement :  adjacent: `adjacent(T;L;x;y)` reverse: `rev(as)` list: `T List` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` iff: `P `⇐⇒` Q` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` member: `t ∈ T` so_lambda: `λ2x.t[x]` so_apply: `x[s]` implies: `P `` Q` top: `Top` prop: `ℙ` iff: `P `⇐⇒` Q` and: `P ∧ Q` uimplies: `b supposing a` false: `False` rev_implies: `P `` Q` decidable: `Dec(P)` or: `P ∨ Q` assert: `↑b` ifthenelse: `if b then t else f fi ` btrue: `tt` less_than: `a < b` squash: `↓T` less_than': `less_than'(a;b)` cons: `[a / b]` bfalse: `ff` not: `¬A` guard: `{T}` ge: `i ≥ j ` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` cand: `A c∧ B` true: `True` append: `as @ bs` so_lambda: `so_lambda(x,y,z.t[x; y; z])` so_apply: `x[s1;s2;s3]` le: `A ≤ B`
Lemmas referenced :  list_induction all_wf iff_wf adjacent_wf reverse_wf list_wf reverse_nil_lemma reverse-cons adjacent-nil nil_wf decidable__lt length_wf length-reverse list-cases null_nil_lemma length_of_nil_lemma product_subtype_list null_cons_lemma length_of_cons_lemma false_wf less_than_wf equal_wf reduce_hd_cons_lemma hd_wf decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermVar_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_wf last-reverse or_wf last_wf cons_wf adjacent-append append_wf itermAdd_wf int_term_value_add_lemma adjacent-cons adjacent-singleton list_ind_nil_lemma non_neg_length
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation lambdaFormation cut thin introduction extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality sqequalRule lambdaEquality cumulativity hypothesis independent_functionElimination rename isect_memberEquality voidElimination voidEquality because_Cache dependent_functionElimination universeEquality independent_pairFormation independent_isectElimination natural_numberEquality unionElimination productElimination imageElimination promote_hyp hypothesis_subsumption equalityTransitivity equalitySymmetry inrFormation productEquality dependent_pairFormation int_eqEquality intEquality computeAll inlFormation imageMemberEquality baseClosed addLevel impliesFunctionality addEquality

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