(tca_3D
(IMP_metric_space_real_fun_TCC1 0
(IMP_metric_space_real_fun_TCC1-1 nil 3563728619
("" (lemma "real_metric_space" ) (("" (inst?) nil nil )) nil )
((fullset const-decl "set" sets nil ) (set type-eq-decl nil sets nil )
(bool nonempty-type-eq-decl nil booleans nil )
(real nonempty-type-from-decl nil reals nil )
(real_pred const-decl "[number_field -> boolean]" reals nil )
(number_field nonempty-type-from-decl nil number_fields nil )
(number_field_pred const-decl "[number -> boolean]" number_fields
nil )
(boolean nonempty-type-decl nil booleans nil )
(number nonempty-type-decl nil numbers nil )
(real_metric_space formula-decl nil real_metric_space "analysis/" ))
nil ))
(cyl_norm_sq_diff_cont 0
(cyl_norm_sq_diff_cont-1 nil 3487000249
("" (skeep)
(("" (lemma "diff_continuous[real,real_dist]" )
((""
(inst - "fullset[real]"
"(LAMBDA (t:real): sqv(vect2(s) + t * vect2(v)) / sq(D))"
"(LAMBDA (t:real): sq(s`z + t * v`z) / sq(H))" )
(("" (expand "-" -)
(("" (assert )
(("" (hide 2)
(("" (lemma "vectors_2D.sqv_add" )
((""
(name "hf1" "(LAMBDA (t:real): sqv(vect2(s))/sq(D))" )
((""
(name "hf2"
"(LAMBDA (t:real): t*(2*vect2(s)*vect2(v)/sq(D)))" )
((""
(name "hf3"
"(LAMBDA (t:real): t*(sqv(vect2(v))/sq(D)))" )
(("" (name "hf4" "(LAMBDA (t:real): t)" )
((""
(case "NOT (LAMBDA (t: real): sqv(vect2(s) + t * vect2(v)) / sq(D)) = hf1 + hf2 + hf3*hf4" )
(("1" (hide 2)
(("1" (hide -5)
(("1"
(decompose-equality +)
(("1"
(hide -)
(("1"
(expand "hf1" +)
(("1"
(expand "hf2" +)
(("1"
(expand "hf3" +)
(("1"
(expand "hf4" +)
(("1" (grind) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2" (replace -1)
(("2"
(name "vf1"
"(LAMBDA (t:real): sq(s`z)/sq(H))" )
(("2"
(name
"vf2"
"(LAMBDA (t:real): t*(2*s`z*v`z/sq(H)))" )
(("2"
(name
"vf3"
"(LAMBDA (t:real): t*(sq(v`z)/sq(H)))" )
(("2"
(name "vf4" "(LAMBDA (t:real): t)" )
(("2"
(case
"NOT (LAMBDA (t: real): sq(s`z + t * v`z) / sq(H)) = vf1 + vf2 + vf3*vf4" )
(("1"
(hide 2)
(("1"
(decompose-equality +)
(("1"
(hide -)
(("1"
(expand "vf1" +)
(("1"
(expand "vf2" +)
(("1"
(expand "vf3" +)
(("1"
(expand "vf4" +)
(("1"
(grind)
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(replace -1)
(("2"
(hide -1)
(("2"
(hide -1)
(("2"
(hide -1)
(("2"
(hide -1)
(("2"
(hide -1)
(("2"
(hide -1)
(("2"
(hide -1)
(("2"
(hide -1)
(("2"
(hide -1)
(("2"
(hide -1)
(("2"
(hide -1)
(("2"
(split
+)
(("1"
(lemma
"sum_continuous[real,real_dist]" )
(("1"
(inst
-
"fullset[real]"
"hf1 + hf2"
"hf3*hf4" )
(("1"
(assert )
(("1"
(hide
2)
(("1"
(split
+)
(("1"
(lemma
"sum_continuous[real,real_dist]" )
(("1"
(inst?)
(("1"
(assert )
(("1"
(hide
2)
(("1"
(split
+)
(("1"
(expand
"continuous?" )
(("1"
(skosimp*)
(("1"
(expand
"continuous_at?" )
(("1"
(skosimp*)
(("1"
(inst
+
"1" )
(("1"
(skosimp*)
(("1"
(expand
"member"
+)
(("1"
(expand
"ball"
+)
(("1"
(expand
"real_dist" )
(("1"
(expand
"hf1"
+)
(("1"
(assert )
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(expand
"hf2" )
(("2"
(name
"cc"
"2*vect2(s)*vect2(v)/sq(D)" )
(("2"
(replace
-1)
(("2"
(case
"cc = 0" )
(("1"
(replace
-1)
(("1"
(hide
-)
(("1"
(grind)
nil
nil ))
nil ))
nil )
("2"
(expand
"continuous?" )
(("2"
(skosimp*)
(("2"
(expand
"continuous_at?" )
(("2"
(skosimp*)
(("2"
(inst
+
"epsilon!1/abs(cc)" )
(("1"
(hide
-)
(("1"
(skosimp*)
(("1"
(expand
"member" )
(("1"
(expand
"ball" )
(("1"
(expand
"real_dist" )
(("1"
(lemma
"abs_mult" )
(("1"
(inst
-
"cc"
"x!1-y!1" )
(("1"
(assert )
(("1"
(replace
-1)
(("1"
(cross-mult
-2)
(("1"
(assert )
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(case
"epsilon!1/abs(cc) > 0" )
(("1"
(assert )
nil
nil )
("2"
(cross-mult
1)
(("2"
(assert )
nil
nil ))
nil )
("3"
(assert )
nil
nil ))
nil )
("3"
(assert )
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(lemma
"prod_continuous[real,real_dist]" )
(("2"
(inst?)
(("2"
(assert )
(("2"
(hide
2)
(("2"
(split
+)
(("1"
(expand
"hf3" )
(("1"
(name
"cc"
"sqv(vect2(v))/sq(D)" )
(("1"
(replace
-1)
(("1"
(case
"cc = 0" )
(("1"
(replace
-1)
(("1"
(hide
-)
(("1"
(grind)
nil
nil ))
nil ))
nil )
("2"
(expand
"continuous?" )
(("2"
(skosimp*)
(("2"
(expand
"continuous_at?" )
(("2"
(skosimp*)
(("2"
(inst
+
"epsilon!1/abs(cc)" )
(("1"
(hide
-)
(("1"
(skosimp*)
(("1"
(expand
"member" )
(("1"
(expand
"ball" )
(("1"
(expand
"real_dist" )
(("1"
(lemma
"abs_mult" )
(("1"
(inst
-
"cc"
"x!1-y!1" )
(("1"
(assert )
(("1"
(replace
-1)
(("1"
(cross-mult
-2)
(("1"
(assert )
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(case
"epsilon!1/abs(cc) > 0" )
(("1"
(assert )
nil
nil )
("2"
(cross-mult
1)
(("2"
(assert )
nil
nil ))
nil )
("3"
(assert )
nil
nil ))
nil )
("3"
(assert )
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(expand
"hf4" )
(("2"
(expand
"continuous?" )
(("2"
(skosimp*)
(("2"
(expand
"continuous_at?" )
(("2"
(skosimp*)
(("2"
(inst
+
"epsilon!1" )
(("2"
(skosimp*)
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(lemma
"sum_continuous[real,real_dist]" )
(("2"
(inst?)
(("2"
(assert )
(("2"
(hide
2)
(("2"
(split)
(("1"
(lemma
"sum_continuous[real,real_dist]" )
(("1"
(inst?)
(("1"
(assert )
(("1"
(hide
2)
(("1"
(split)
(("1"
(expand
"vf1" )
(("1"
(grind
:exclude
("fullset"
"sq" ))
nil
nil ))
nil )
("2"
(expand
"vf2" )
(("2"
(name
"cc"
"(2 * (s`z * v`z) / sq(H))" )
(("2"
(replace
-1)
(("2"
(case
"cc = 0" )
(("1"
(replace
-1)
(("1"
(hide
-)
(("1"
(grind)
nil
nil ))
nil ))
nil )
("2"
(expand
"continuous?" )
(("2"
(skosimp*)
(("2"
(expand
"continuous_at?" )
(("2"
(skosimp*)
(("2"
(inst
+
"epsilon!1/abs(cc)" )
(("1"
(hide
-)
(("1"
(skosimp*)
(("1"
(expand
"member" )
(("1"
(expand
"ball" )
(("1"
(expand
"real_dist" )
(("1"
(lemma
"abs_mult" )
(("1"
(inst
-
"cc"
"x!1-y!1" )
(("1"
(assert )
(("1"
(replace
-1)
(("1"
(cross-mult
-2)
(("1"
(assert )
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(case
"epsilon!1/abs(cc) > 0" )
(("1"
(assert )
nil
nil )
("2"
(cross-mult
1)
(("2"
(assert )
nil
nil ))
nil )
("3"
(assert )
nil
nil ))
nil )
("3"
(assert )
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(lemma
"prod_continuous[real,real_dist]" )
(("2"
(inst?)
(("2"
(assert )
(("2"
(hide
2)
(("2"
(split)
(("1"
(expand
"vf3" )
(("1"
(name
"cc"
"sq(v`z)/sq(H)" )
(("1"
(replace
-1)
(("1"
(case
"cc = 0" )
(("1"
(replace
-1)
(("1"
(hide
-)
(("1"
(grind)
nil
nil ))
nil ))
nil )
("2"
(expand
"continuous?" )
(("2"
(skosimp*)
(("2"
(expand
"continuous_at?" )
(("2"
(skosimp*)
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