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lemma bi_unique_rel_set_bij_betw:
assumes unique: "bi_unique R"
and rel: "rel_set R A B"
shows "\<exists>f. bij_betw f A B \<and> (\<forall>x\<in>A. R x (f x))" |
lemma BinOpThrow1':
"P,E \<turnstile> \<langle>e\<^sub>1,s\<^sub>0\<rangle> \<Rightarrow>' \<langle>throw e,s\<^sub>1\<rangle> \<Longrightarrow>
P,E \<turnstile> \<langle>e\<^sub>1 \<guillemotleft>bop\<guillemotright> e\<^sub>2, s\<^sub>0\<rangle> \<Rightarrow>' \<langle>throw e,s\<^sub>1\<rangle>" |
lemma Subst_not_Nil:
assumes "v \<noteq> \<^bold>\<sharp>" and "t \<noteq> \<^bold>\<sharp>"
shows "t \<noteq> \<^bold>\<sharp> \<Longrightarrow> Subst n v t \<noteq> \<^bold>\<sharp>" |
lemma listrelp_imp_listsp1:
assumes H: "listrelp (\<lambda>x y. P x) xs ys"
shows "listsp P xs" |
lemma phis'_aux_finite:
assumes "finite (Mapping.keys phis)"
shows "finite (Mapping.keys (phis'_aux g v ns phis))" |
lemma free_ag_single:"\<lbrakk>commute_bpp f (aug_pm_set z i {a});
assoc_bpp (aug_pm_set z i {a}) f; ipp_cond1 {a} i; ipp_cond2 z {a} i f;
ipp_cond3 z i; inv_ipp z i f {a}; commute_bpp f (aug_pm_set z i {a});
zeroA z i f {a} z; free_gen_condition f i a z; n \<noteq> m\<rbrakk> \<Longrightarrow>
(n\<Odot>a\<^bsub>f,i,z\<^esub>) \<noteq> (m\<Odot>a\<^bsub>f,i,z\<^esub>)" |
lemma infinite_finite_Inter:
assumes "finite \<A>" "\<A>\<noteq>{}" "\<And>A. A \<in> \<A> \<Longrightarrow> infinite A"
and "\<And>A B. \<lbrakk>A \<in> \<A>; B \<in> \<A>\<rbrakk> \<Longrightarrow> A \<inter> B \<in> \<A>"
shows "infinite (\<Inter>\<A>)" |
lemma wf_darcs_to_dtree_aux1: "r \<notin> verts T \<Longrightarrow> wf_darcs (to_dtree_aux r)" |
lemma equivalence_data_in_hom\<^sub>B [intro]:
assumes "B.obj a"
shows "\<guillemotleft>e a : a \<rightarrow>\<^sub>B P\<^sub>0 a\<guillemotright>" and "\<guillemotleft>d a : P\<^sub>0 a \<rightarrow>\<^sub>B a\<guillemotright>"
and "\<guillemotleft>e a : e a \<Rightarrow>\<^sub>B e a\<guillemotright>" and "\<guillemotleft>d a : d a \<Rightarrow>\<^sub>B d a\<guillemotright>"
and "\<guillemotleft>\<eta> a : a \<rightarrow>\<^sub>B a\<guillemotright>" and "\<guillemotleft>\<epsilon> a : P\<^sub>0 a \<rightarrow>\<^sub>B P\<^sub>0 a\<guillemotright>"
and "\<guillemotleft>\<eta> a : a \<Rightarrow>\<^sub>B d a \<star>\<^sub>B e a\<guillemotright>" and "\<guillemotleft>\<epsilon> a : e a \<star>\<^sub>B d a \<Rightarrow>\<^sub>B P\<^sub>0 a\<guillemotright>" |
lemma (in Group) normal_closure:
assumes "A\<subseteq>G"
shows "normal (normal_closure A)" |
lemma strong_confluentp_ACI: "strong_confluentp (~)" |
lemma hull_Un_subset: "(S hull s) \<union> (S hull t) \<subseteq> (S hull (s \<union> t))" |
lemma word_plus_mono_right: "y \<le> z \<Longrightarrow> x \<le> x + z \<Longrightarrow> x + y \<le> x + z"
for x y z :: "'a::len word" |
lemma Hash_imp_parts2 [rule_format]:
"evs \<in> set_cr
==> Hash\<lbrace>X, Nonce M, Y, Nonce N\<rbrace> \<in> parts (knows Spy evs) \<longrightarrow>
Nonce M \<in> parts (knows Spy evs) \<and> Nonce N \<in> parts (knows Spy evs)" |
lemma delete1_correct:
"(delete1,RETURN o delete) \<in> gap_rel \<rightarrow> \<langle>gap_rel\<rangle>nres_rel" |
lemma word_plus_mcs_4':
fixes x :: "'a :: len word"
shows "\<lbrakk>x + v \<le> x + w; x \<le> x + v\<rbrakk> \<Longrightarrow> v \<le> w" |
lemma Can_and_Nml_implies_Ide:
assumes "Can t" and "Nml t"
shows "Ide t" |
lemma length_dropWhile [termination_simp]: "length (dropWhile P xs) \<le> length xs" |
lemma lspasl_p_der:
"(h1,h2\<triangleright>h0) \<Longrightarrow> (h1,h2\<triangleright>h3) \<Longrightarrow> (h1,h2\<triangleright>h0) \<and> h0 = h3" |
lemma oneH:"\<one> \<in> H" |
lemma int_shiftr_numeral [simp]:
"drop_bit (numeral w') (1 :: int) = 0"
"drop_bit (numeral w') (numeral num.One :: int) = 0"
"drop_bit (numeral w') (numeral (num.Bit0 w) :: int) = drop_bit (pred_numeral w') (numeral w)"
"drop_bit (numeral w') (numeral (num.Bit1 w) :: int) = drop_bit (pred_numeral w') (numeral w)"
"drop_bit (numeral w') (- numeral (num.Bit0 w) :: int) = drop_bit (pred_numeral w') (- numeral w)"
"drop_bit (numeral w') (- numeral (num.Bit1 w) :: int) = drop_bit (pred_numeral w') (- numeral (Num.inc w))" |
lemma program_result_measure':
"qbs_prob_measure (qbs_prob_space (exp_qbs \<real>\<^sub>Q \<real>\<^sub>Q, (\<lambda>(s, b) r. s * r + b) \<circ> real_real.g, density (distr (\<nu> \<Otimes>\<^sub>M \<nu>) real_borel real_real.f) (\<lambda>r. (obs \<circ> (\<lambda>(s, b) r. s * r + b) \<circ> real_real.g) r / C)))
= distr (density (\<nu> \<Otimes>\<^sub>M \<nu>) (\<lambda>(s,b). obs (\<lambda>r. s * r + b) / C)) (qbs_to_measure (exp_qbs \<real>\<^sub>Q \<real>\<^sub>Q)) (\<lambda>(s, b) r. s * r + b)" |
lemma tape_of_ex1[intro]:
"\<exists>rna ml. Oc \<up> a @ Bk \<up> rn = <ml::nat list> @ Bk \<up> rna \<or> Oc \<up> a @ Bk \<up> rn = Bk # <ml> @ Bk \<up> rna" |
lemma outputTauTrans[dest]:
fixes a :: name
and b :: name
and P :: pi
and P' :: pi
assumes "a{b}.P \<longmapsto>\<tau> \<prec> P'"
shows False |
lemma dirichlet_prod'_inversion2:
assumes "\<forall>x\<ge>1. f x = dirichlet_prod' ainv g x" "x \<ge> 1"
"dirichlet_prod a ainv = (\<lambda>n. if n = 1 then 1 else 0)"
shows "g x = dirichlet_prod' a f x" |
lemma cl_ident: "r\<in>L ==> cl L r = r" |
lemma to_int_vec_index[simp]: "i < dim_vec v \<Longrightarrow> (to_int_vec v $i) = to_int_mod_ring (v $i)" |
lemma punit_sminus [simp]: "punit.sminus = (-)" |
lemma wf_max0: "x \<in> carrier R \<Longrightarrow> Max \<zero> x \<in> carrier R" |
lemma [code_abbrev]:
"(real_of_float (of_int a) :: real) = (Ratreal (Rat.of_int a) :: real)" |
lemma (in Module) l_comb_transpos:" \<lbrakk>ideal R A; H \<subseteq> carrier M;
s \<in> {l. l \<le> Suc n} \<rightarrow> A; f \<in> {l. l \<le> Suc n} \<rightarrow> H;
j < Suc n \<rbrakk> \<Longrightarrow>
\<Sigma>\<^sub>e M (cmp (\<lambda>k. s k \<cdot>\<^sub>s f k) (transpos j (Suc n))) (Suc n) =
\<Sigma>\<^sub>e M (\<lambda>k. (cmp s (transpos j (Suc n))) k \<cdot>\<^sub>s
(cmp f (transpos j (Suc n))) k) (Suc n)" |
lemma zero_applied_to [simp]:
"(0::('a \<Rightarrow> ('b::real_vector))) x = 0" |
lemma ldistinct_coinduct [consumes 1, case_names ldistinct, case_conclusion ldistinct lhd ltl, coinduct pred: ldistinct]:
assumes "X xs"
and step: "\<And>xs. \<lbrakk> X xs; \<not> lnull xs \<rbrakk>
\<Longrightarrow> lhd xs \<notin> lset (ltl xs) \<and> (X (ltl xs) \<or> ldistinct (ltl xs))"
shows "ldistinct xs" |
lemma alwaysE: "\<lbrakk>(\<box>P) \<sigma>; P (\<sigma> |\<^sub>s i) \<Longrightarrow> Q\<rbrakk> \<Longrightarrow> Q" |
lemma finite'_code [code]:
"finite' (set xs) \<longleftrightarrow> True"
"finite' (List.coset xs) \<longleftrightarrow> of_phantom (finite_UNIV :: 'a finite_UNIV)" |
lemma ack_le_mono2: "j \<le> k \<Longrightarrow> ack i j \<le> ack i k" |
lemma dtree_coinduct[elim, consumes 1, case_names Lift, induct pred: "HOL.eq"]:
assumes phi: "\<phi> tr1 tr2" and
Lift: "\<And> tr1 tr2. \<phi> tr1 tr2 \<Longrightarrow>
root tr1 = root tr2 \<and> rel_set (rel_sum (=) \<phi>) (cont tr1) (cont tr2)"
shows "tr1 = tr2" |
lemma of_rat_sum: "of_rat (\<Sum>a\<in>A. f a) = (\<Sum>a\<in>A. of_rat (f a))" |
lemma in_rangeC_singleton: "f x \<in> rangeC {f}" |
lemma numsubst0_I:
shows "Inum (b#bs) (numsubst0 a t) = Inum ((Inum (b#bs) a)#bs) t" |
lemma is_in_insort: "y \<in> set xs \<Longrightarrow> y \<in> set (insort x xs l)" |
lemma (in \<Z>) ntcf_Set_obj_coprod_is_tm_cat_obj_coprod:
\<comment>\<open>See Theorem 5.2 in Chapter Introduction in \cite{hungerford_algebra_2003}.\<close>
assumes "VLambda I F \<in>\<^sub>\<circ> Vset \<alpha>"
shows "ntcf_Set_obj_coprod \<alpha> I F :
F >\<^sub>C\<^sub>F\<^sub>.\<^sub>t\<^sub>m\<^sub>.\<^sub>\<Coprod> (\<Coprod>\<^sub>\<circ>i\<in>\<^sub>\<circ>I. F i) : I \<mapsto>\<mapsto>\<^sub>C\<^sub>.\<^sub>t\<^sub>m\<^bsub>\<alpha>\<^esub> cat_Set \<alpha>" |
lemma action_order_is_new_actionD:
"\<lbrakk> E \<turnstile> a \<le>a a'; is_new_action (action_obs E a') \<rbrakk> \<Longrightarrow> is_new_action (action_obs E a)" |
lemma has_field_derivative_subset:
"(f has_field_derivative y) (at x within s) \<Longrightarrow> t \<subseteq> s \<Longrightarrow>
(f has_field_derivative y) (at x within t)" |
lemma tau_om2 [simp]: "\<tau> x\<^sup>\<omega> = \<tau> x" |
lemma evalF_subF_eq: "!phi theta. evalF M phi (subF theta A) = evalF M (phi o theta) A" |
lemma \<alpha>edges_finite[simp, intro!]: "invar g \<Longrightarrow> finite (\<alpha>edges_aux g)" |
lemma lemma_2_7_23: "(a r\<rightarrow> b) * (c r\<rightarrow> d) \<le> (a \<sqinter> c) r\<rightarrow> (b \<sqinter> d)" |
lemma summable_in_conv_radius:
fixes f :: "nat \<Rightarrow> 'a :: {banach, real_normed_div_algebra}"
assumes "ereal (norm z) < conv_radius f"
shows "summable (\<lambda>n. f n * z ^ n)" |
lemma of_bool_Bex_eq_nn_integral:
assumes unique: "\<And>x y. x \<in> X \<Longrightarrow> y \<in> X \<Longrightarrow> P x \<Longrightarrow> P y \<Longrightarrow> x = y"
shows "of_bool (\<exists>y\<in>X. P y) = (\<integral>\<^sup>+y. of_bool (P y) \<partial>count_space X)" |
lemma induced_automorphism_fixespointwise_C0_int_D0:
"fixespointwise \<s> (C0\<inter>D0)" |
lemma coneI: "p = a * h \<Longrightarrow> a \<in> P[U] \<Longrightarrow> p \<in> cone (h, U)" |
lemma take_bit_or [simp]:
\<open>take_bit n (a OR b) = take_bit n a OR take_bit n b\<close> |
lemma tm_skip_first_arg_correct_Nil:
"\<lbrace>\<lambda>tap. tap = ([], [])\<rbrace> tm_skip_first_arg \<lbrace>\<lambda>tap. tap = ([], [Bk]) \<rbrace>" |
lemma W_continuous_on: "continuous_on (Sigma X existence_ivl0) (\<lambda>(x0, t). Dflow x0 t)"
\<comment> \<open>TODO: somewhere here is hidden continuity wrt rhs of ODE, extract it!\<close> |
lemma Inr_in_sum_iff [iff]: "Inr b \<in> elts (A \<Uplus> B) \<longleftrightarrow> b \<in> elts B" |
lemma simulation_silent2_aux:
"\<lbrakk> s1 \<approx> s2; s2 -\<tau>2\<rightarrow> s2' \<rbrakk> \<Longrightarrow> s1 \<approx> s2' \<and> \<mu>2\<^sup>+\<^sup>+ s2' s2 \<or> (\<exists>s1'. s1 -\<tau>1\<rightarrow>+ s1' \<and> s1' \<approx> s2')" |
lemma gen_boolean_algebra_idempotent:
assumes "S = \<Union> Xs"
shows "gen_boolean_algebra S (gen_boolean_algebra S Xs) = (gen_boolean_algebra S Xs)" |
lemma silent_moves_nonempty_nodestack_False:
assumes "S,kind \<turnstile> ([m],[cf]) =as\<Rightarrow>\<^sub>\<tau> (m'#ms',s')" and "valid_node m"
and "ms' \<noteq> []" and "CFG_node m' \<in> sum_SDG_slice1 nx" and "nx \<in> S"
shows False |
lemma "do x \<leftarrow> return 1;
return (2::nat);
return x
od =
return 1 >>=
(\<lambda>x. return (2::nat) >>=
K_bind (return x))" |
lemma scaleC_right_mono_neg: "b \<le> a \<Longrightarrow> c \<le> 0 \<Longrightarrow> a *\<^sub>C c \<le> b *\<^sub>C c"
for c :: "'a::ordered_complex_vector" |
lemma minGraphProps9':
"minGraphProps g \<Longrightarrow> f \<in> \<F> g \<Longrightarrow> v \<in> \<V> f \<Longrightarrow> v < countVertices g" |
lemma (in wf_sub_rel) extends_imp_wf_sub_rel :
assumes "extends g subs sub subs'"
shows "wf_sub_rel subs'" |
lemma permutes_funpow:
assumes "p permutes S" shows "(p ^^ n) permutes S" |
lemma sup_acc_app_cong: "j \<le> length rho \<Longrightarrow> sup_acc step accept (rho @ [x]) q i j =
sup_acc step accept rho q i j" |
lemma has_integral_implies_lebesgue_measurable_cbox:
fixes f :: "'a :: euclidean_space \<Rightarrow> real"
assumes f: "(f has_integral I) (cbox x y)"
shows "f \<in> lebesgue_on (cbox x y) \<rightarrow>\<^sub>M borel" |
lemma dtail_f_alt_commute:
assumes "P = (\<lambda>xs. wf_darcs (Node r xs))"
and "Q = (\<lambda>(t1,e1) b. e \<in> darcs t1)"
and "R = (\<lambda>(t1,e1) b. dtail t1 def)"
shows "comp_fun_commute (\<lambda>a b. if a \<notin> fset xs \<or> \<not> Q a b \<or> \<not> P xs then b else R a b)" |
lemma dbm_not_lt_eq: "\<not> a \<prec> b \<Longrightarrow> \<not> b \<prec> a \<Longrightarrow> a = b" |
theorem HStartBallot_HInv1:
assumes inv1: "HInv1 s"
and act: "HStartBallot s s' p"
shows "HInv1 s'" |
lemma MExit_correct:
assumes wf: "wf_prog wt P"
assumes meth: "P \<turnstile> C sees M:Ts\<rightarrow>T=\<lfloor>(mxs,mxl\<^sub>0,ins,xt)\<rfloor> in C"
assumes ins: "ins!pc = MExit"
assumes wt: "P,T,mxs,size ins,xt \<turnstile> ins!pc,pc :: \<Phi> C M"
assumes conf: "\<Phi> \<turnstile> t: (None, h, (stk,loc,C,M,pc)#frs)\<surd>"
assumes no_x: "(tas, \<sigma>) \<in> exec_instr (ins!pc) P t h stk loc C M pc frs"
shows "\<Phi> \<turnstile> t: \<sigma> \<surd>" |
lemma points_index_one_not_unique_block:
assumes "B index ps = 1"
assumes "ps \<subseteq> bl"
assumes "bl \<in># B"
assumes "bl' \<in># B - {#bl#}"
shows "\<not> ps \<subseteq> bl'" |
lemma collect_locksI:
"Lock \<in> set (las $ l) \<Longrightarrow> l \<in> collect_locks las" |
lemma distinct_fst_half_segments:
"distinct (map fst (half_segments_of_aform X))" |
lemma mkCone_cone:
assumes "cone a \<chi>"
shows "mkCone (\<chi> J.FF) (\<chi> J.TT) = \<chi>" |
lemma (in BlueDFS_invar) red_DFS_precond_aux:
assumes BI: "blue_basic_invar s"
assumes [simp]: "lasso s = None"
assumes SNE: "stack s \<noteq> []"
shows
"fb_graph (G \<lparr> g_V0 := {hd (stack s)} \<rparr>)"
and "fb_graph (G \<lparr> g_E := E \<inter> UNIV \<times> - red s, g_V0 := {hd (stack s)} \<rparr>)"
and "restr_invar E (red s) (\<lambda>x. x \<in> set (stack s))" |
lemma lookup_hnr_aux: "(uncurry lookup,uncurry (RETURN oo op_map_lookup)) \<in> id_assn\<^sup>k *\<^sub>a is_map\<^sup>k \<rightarrow>\<^sub>a id_assn" |
lemma is_mult_sum4sq_nat: "is_sum4sq_nat x \<Longrightarrow> is_sum4sq_nat y \<Longrightarrow> is_sum4sq_nat (x*y)" |
lemma Form_quot_fm [iff]: fixes A :: fm shows "Form \<lbrakk>\<guillemotleft>A\<guillemotright>\<rbrakk>e" |
lemma attach_shadow_root_element_ptr_in_heap:
assumes "h \<turnstile> ok (attach_shadow_root element_ptr shadow_root_mode)"
shows "element_ptr |\<in>| element_ptr_kinds h" |
lemma starts:
fixes i j
assumes "\<I> i" and "\<I> j"
shows "((i,j) \<in> s \<union> s^-1 \<union> e) = (BEGIN i = BEGIN j)" |
lemma (in normalization_semidom) factorial_semiring_altI_aux:
assumes finite_divisors: "\<And>x. x \<noteq> 0 \<Longrightarrow> finite {y. y dvd x \<and> normalize y = y}"
assumes irreducible_imp_prime_elem: "\<And>x. irreducible x \<Longrightarrow> prime_elem x"
assumes "x \<noteq> 0"
shows "\<exists>A. (\<forall>x. x \<in># A \<longrightarrow> prime_elem x) \<and> normalize (prod_mset A) = normalize x" |
lemma sgn2_eq_1_sub_arg: "sgn2 = (\<lambda> x. 1 - x)" |
lemma (in Gromov_hyperbolic_space_geodesic) proj_along_geodesic_contraction:
assumes "geodesic_segment G" "px \<in> proj_set x G" "py \<in> proj_set y G"
shows "dist px py \<le> max (5 * deltaG(TYPE('a))) (dist x y - dist px x - dist py y + 10 * deltaG(TYPE('a)))" |
lemma greaterThanLessThan_eq: "{a<\<^sub>a..<\<^sub>ab} = {a<\<^sub>a..} \<inter> {..<\<^sub>ab}" |
lemma matrix_change_of_basis_mat_1:
fixes X::"'a::{field}^'n^'n"
assumes basis_X: "is_basis (set_of_vector X)"
shows "matrix_change_of_basis X X = mat 1" |
lemma tendsto_neg_powr_complex_of_nat:
assumes "filterlim f at_top F" and "Re s < 0"
shows "((\<lambda>x. of_nat (f x) powr s) \<longlongrightarrow> 0) F" |
lemma continuous_closed_quotient_map:
"\<lbrakk>continuous_map X X' f; closed_map X X' f\<rbrakk> \<Longrightarrow> quotient_map X X' f \<longleftrightarrow> f ` (topspace X) = topspace X'" |
lemma wf_inst_formula:
assumes "wf_fmla (ty_term Q constT) \<phi>"
shows "wf_fmla objT ((map_formula o map_atom o subst_term) f \<phi>)" |
lemma take_length_ib[simp]:
assumes "0 < j" "j \<le> length s"
shows "take (length (intrinsic_border (take j s))) s = intrinsic_border (take j s)" |
lemma
assumes "invariant_1 plr"
defines "x \<equiv> the_unique_root plr" and "p \<equiv> poly_real_alg_1 plr" and "l \<equiv> rai_lb plr" and "r \<equiv> rai_ub plr"
shows invariant_1D: "root_cond plr x"
"sgn l = sgn r" "sgn x = of_rat (sgn r)" "unique_root plr" "poly_cond p" "degree p > 0" "primitive p"
and invariant_1_root_cond: "\<And> y. root_cond plr y \<longleftrightarrow> y = x" |
lemma gmn_correct:
assumes "is_measured_node nd"
shows "gmn nd = sum_list (map snd (nodeToList nd))" |
lemma density_context_equiv:
assumes "\<And>\<sigma>. \<sigma> \<in> space (state_measure (V \<union> V') \<Gamma>) \<Longrightarrow> \<delta> \<sigma> = \<delta>' \<sigma>"
assumes [simp, measurable]: "\<delta>' \<in> borel_measurable (state_measure (V \<union> V') \<Gamma>)"
assumes "density_context V V' \<Gamma> \<delta>"
shows "density_context V V' \<Gamma> \<delta>'" |
lemma update_assignment_alt: "update_assignment u as = update_assignment_alt u as" |
lemma assoc_ell2'_assoc_ell2[simp]: \<open>assoc_ell2' o\<^sub>C\<^sub>L assoc_ell2 = id_cblinfun\<close> |
lemma if_SE_split_asm : " (\<sigma> \<Turnstile> if\<^sub>S\<^sub>E P B\<^sub>1 B\<^sub>2) = ((P \<sigma> \<and> (\<sigma> \<Turnstile> B\<^sub>1)) \<or> (\<not> P \<sigma> \<and> (\<sigma> \<Turnstile> B\<^sub>2)))" |
lemma funpower_fixespointwise:
assumes "fixespointwise f A"
shows "fixespointwise (f^^n) A" |
lemma wcode_double_case:
shows "\<exists>stp ln rn. steps0 (Suc 0, Bk # Bk\<up>(m) @ Oc # Oc # ires, Bk # Oc\<up>(Suc rs) @ Bk\<up>(n)) wcode_main_tm stp =
(Suc 0, Bk # Bk\<up>(ln) @ Oc # ires, Bk # Oc\<up>(Suc (2 * rs + 2)) @ Bk\<up>(rn))"
(is "\<exists>stp ln rn. ?tm stp ln rn") |
lemma ideduct_subst: "M \<turnstile> t \<Longrightarrow> M \<cdot>\<^sub>s\<^sub>e\<^sub>t \<delta> \<turnstile> t \<cdot> \<delta>" |
lemma lspasl_c_eq:
"((h1,h2\<triangleright>h0) \<and> (h1,h3\<triangleright>h0)) = ((h1,h2\<triangleright>h0) \<and> h2 = h3)" |
lemma tarski_aux:
assumes "R - 1\<^sub>\<pi> \<noteq> {}"
and "(a,A) \<in> NC"
shows "(a,A) \<in> NC \<cdot> ((R - 1\<^sub>\<pi>) \<cdot> NC)" |
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