#A; #F; #a; #H; ncases H; /2/.
nqed.
-alias symbol "I" (instance 7) = "I".
-alias symbol "I" (instance 18) = "I".
-alias symbol "I" (instance 18) = "I".
-alias symbol "I" (instance 18) = "I".
+(* XXX: disambiguation crazy *)
+alias id "I" = "cic:/matita/ng/topology/igft/I.fix(0,0,2)".
nlet corec ftfish_coind
(A: Ax_pro) (F: Ω^A) (P: A → CProp[0])
- (Hcorefl: ∀a. P a → a ∈ F)
- (Hcoleqleft: ∀a. P a → ∀b. a ≤ b → P b)
- (Hcoleqinfinity: ∀a. P a → ∀b. a ≤ b → ∀i:𝐈 b. ∃x. x ∈ 𝐂 b i ↓ (singleton … a) ∧ P x)
+ (Hcorefl: ∀a:A. P a → a ∈ F)
+ (Hcoleqleft: ∀a:A. P a → ∀b:A. pre_r ? (Aleq A) a (*≤*) b → P b)
+ (Hcoleqinfinity: ∀a:A. P a → ∀b:A. pre_r ? (Aleq A) a (*≤*) b → ∀i:I A b. ∃x:A. x ∈ C A b i ↓ {(a)} ∧ P x)
: ∀a:A. P a → a ⋉ F ≝ ?.
#a; #H; @
[ /2/
- | #b; #H; napply (ftfish_coind … Hcorefl Hcoleqleft Hcoleqinfinity); /2/
+ | #b; #H; napply (ftfish_coind ??? Hcorefl Hcoleqleft Hcoleqinfinity); /2/
| #b; #H1; #i; ncases (Hcoleqinfinity a H ? H1 i); #x; *; #H2; #H3;
- @ x; @; //; napply (ftfish_coind … Hcorefl Hcoleqleft Hcoleqinfinity); //]
+ @ x; @; //; napply (ftfish_coind ??? Hcorefl Hcoleqleft Hcoleqinfinity); //]
nqed.
-(*CSC: non serve manco questo (vedi sotto) *)
+(*CSC: non serve manco questo (vedi sotto)
nlemma auto_hint3: ∀A. S__o__AAx A = S (AAx A).
#A; //.
-nqed.
+nqed.*)
alias symbol "I" (instance 6) = "I".
ntheorem ftcoinfinity: ∀A: Ax_pro. ∀F: Ω^A. ∀a. a ⋉ F → (∀i: 𝐈 a. ∃b. b ∈ 𝐂 a i ∧ b ⋉ F).
| @ [ @ (Qminus q 1) (Qplus q 1) | ncases daemon ]
##| #c; #d; #Hc; #Hd; @ [ @ (Qmin (fst … c) (fst … d)) (Qmax (snd … c) (snd … d)) | ncases daemon]
##| #a; #H; napply (ftfish_coind Rax ? (λa. fst … a < q ∧ q < snd … a)); /2/
- [ /5/ | #b; *; #H1; #H2; #c; *; #H3; #H4; #i; ncases i
- [ #w; nnormalize;
- ##| nnormalize;
- ]
+ [ ncases daemon; ##| #b; *; #H1; #H2; #c; *; #H3; #H4; #i; ncases i
+ [ #w; nnormalize; ncases daemon;
+ ##| nnormalize; ncases daemon;
+##]
nqed.