{ [U:Atom  SimpleType]. [x:Atom]. [st:SimpleType].
    st-unifies(U;st_var(x);st) ~ ff 
    supposing (x  st-vars(st))  (st_var?(st)) }

{ Proof }



Definitions occuring in Statement :  st-unifies: st-unifies(U;st1;st2) st-vars: st-vars(st) st_var?: st_var?(x) st_var: st_var(name) simple_type: SimpleType assert: b bfalse: ff uimplies: b supposing a uall: [x:A]. B[x] not: A and: P  Q function: x:A  B[x] atom: Atom sqequal: s ~ t l_member: (x  l)
Definitions :  decide: case b of inl(x) =s[x] | inr(y) =t[y] ifthenelse: if b then t else f fi  subtype: S  T suptype: suptype(S; T) set: {x:A| B[x]}  rev_uimplies: rev_uimplies(P;Q) st_var: st_var(name) st-subst: st-subst(subst;st) eq_bool: p =b q lt_int: i <z j le_int: i z j eq_int: (i = j) eq_atom: x =a y null: null(as) set_blt: a < b grp_blt: a < b apply: f a infix_ap: x f y dcdr-to-bool: [d] bl-all: (xL.P[x])_b bl-exists: (xL.P[x])_b b-exists: (i<n.P[i])_b eq_type: eq_type(T;T') eq_atom: eq_atom$n(x;y) qeq: qeq(r;s) q_less: q_less(r;s) q_le: q_le(r;s) deq-member: deq-member(eq;x;L) deq-disjoint: deq-disjoint(eq;as;bs) deq-all-disjoint: deq-all-disjoint(eq;ass;bs) eq_id: a = b eq_lnk: a = b es-eq-E: e = e' es-bless: e <loc e' es-ble: e loc e' st-similar: st-similar(st1;st2) bimplies: p  q band: p  q bnot: b bor: p q st-vars: st-vars(st) eclass: EClass(A[eo; e]) bfalse: ff pair: <a, b> fpf: a:A fp-B[a] void: Void false: False st_var?: st_var?(x) st_const?: st_const?(x) st_arrow?: st_arrow?(x) st_prod?: st_prod?(x) st_union?: st_union?(x) st_list?: st_list?(x) st_class?: st_class?(x) simple_type_ind_st_var: simple_type_ind_st_var_compseq_tag_def st_var-name: st_var-name(x) exists: x:A. B[x] rec: rec(x.A[x]) strong-subtype: strong-subtype(A;B) le: A  B ge: i  j  less_than: a < b uiff: uiff(P;Q) guard: {T} implies: P  Q universe: Type equal: s = t sq_type: SQType(T) bool: st-unifies: st-unifies(U;st1;st2) subtype_rel: A r B all: x:A. B[x] function: x:A  B[x] product: x:A  B[x] not: A assert: b l_member: (x  l) prop: and: P  Q atom: Atom uimplies: b supposing a sqequal: s ~ t uall: [x:A]. B[x] member: t  T simple_type: SimpleType isect: x:A. B[x] Auto: Error :Auto,  D: Error :D,  THENM: Error :THENM,  CollapseTHEN: Error :CollapseTHEN,  RepUR: Error :RepUR,  tactic: Error :tactic,  st-rank: st-rank(st) natural_number: $n RepeatFor: Error :RepeatFor,  simple_type_ind_st_class: simple_type_ind_st_class_compseq_tag_def simple_type_ind_st_list: simple_type_ind_st_list_compseq_tag_def simple_type_ind_st_union: simple_type_ind_st_union_compseq_tag_def simple_type_ind_st_prod: simple_type_ind_st_prod_compseq_tag_def add: n + m limited-type: LimitedType btrue: tt unit: Unit imax: imax(a;b) cand: A c B atom-deq: AtomDeq simple_type_ind_st_arrow: simple_type_ind_st_arrow_compseq_tag_def simple_type_ind_st_const: simple_type_ind_st_const_compseq_tag_def real: grp_car: |g| nat: int: true: True IdLnk: IdLnk Id: Id rationals: so_apply: x[s] or: P  Q append: as @ bs locl: locl(a) Knd: Knd iff: P  Q l-union: as  bs list: type List nil: [] cons: [car / cdr] union: left + right Unfold: Error :Unfold,  Try: Error :Try,  ORELSE: Error :ORELSE,  CollapseTHENA: Error :CollapseTHENA,  base: Base so_lambda: x.t[x]
Lemmas :  rec_subtype_base base_wf subtype_rel_wf product_subtype_base union_subtype_base st-subst-rank nat_wf st-rank_wf le_wf assert_of_le_int eqtt_to_assert uiff_transitivity member-union atom-deq_wf l-union_wf nil_member true_wf atom_subtype_base member_singleton assert_functionality_wrt_uiff bnot_of_le_int assert_of_lt_int lt_int_wf bnot_wf le_int_wf st-similar-rank l_member_wf st-vars_wf st_var_wf simple_type_wf member_wf st-subst_wf st-similar_wf assert_wf false_wf not_wf assert_of_bnot eqff_to_assert st_var?_wf bfalse_wf st-unifies_wf bool_wf bool_subtype_base subtype_base_sq

\mforall{}[U:Atom  {}\mrightarrow{}  SimpleType].  \mforall{}[x:Atom].  \mforall{}[st:SimpleType].
    st-unifies(U;st\_var(x);st)  \msim{}  ff  supposing  (x  \mmember{}  st-vars(st))  \mwedge{}  (\mneg{}\muparrow{}st\_var?(st))


Date html generated: 2011_08_17-PM-04_58_38
Last ObjectModification: 2011_02_08-PM-12_17_15

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