| We_need_to_prove (_, term, ident, term1) -> "we need to prove" ^ term_pp term ^ "(" ^ ident ^ ")" ^ (match term1 with None -> " " | Some term1 -> term_pp term1)
| We_proceed_by_induction_on (_, term, term1) -> "we proceed by induction on" ^ term_pp term ^ "to prove" ^ term_pp term1
| Byinduction (_, term, ident) -> "by induction hypothesis we know" ^ term_pp term ^ "(" ^ ident ^ ")"
- | Thesisbecomes (_, term) -> "the thesis becomes" ^ term_pp term
- | Let1 (_, ident, term, term1) -> "let" ^ ident ^ ":" ^ term_pp term ^ "such that" ^ term_pp term1
- | Bywehave (_, term, term1, ident, term2, ident1) -> "by" ^ (match term with None -> "_" | Some term -> term_pp term) ^ "we have" ^ term_pp term1 ^ "(" ^ ident ^ ")" ^ "and" ^ term_pp term2 ^ "(" ^ ident1 ^ ")"
- | RewritingStep (_, term, term1, term2 ) -> (match term with None -> " " | Some term -> "obtain " ^ term_pp term) ^ "=" ^ term_pp term1 ^ (match term2 with None -> "_" | Some term2 -> term_pp term2 )
+ | Thesisbecomes (_, term) -> "the thesis becomes " ^ term_pp term
+ | ExistsElim (_, term0, ident, term, ident1, term1) -> "by " ^ term_pp term0 ^ "let " ^ ident ^ ":" ^ term_pp term ^ "such that " ^ term_pp term1 ^ "(" ^ ident1 ^ ")"
+ | AndElim (_, term, ident1, term1, ident2, term2) -> "by " ^ term_pp term ^ "we have " ^ term_pp term1 ^ " (" ^ ident1 ^ ") " ^ "and " ^ term_pp term2 ^ " (" ^ ident2 ^ ")"
+ | RewritingStep (_, term, term1, term2, cont) -> (match term with None -> " " | Some term -> "obtain " ^ term_pp term) ^ "=" ^ term_pp term1 ^ (match term2 with None -> "_" | Some term2 -> term_pp term2) ^ (match cont with None -> " done" | Some Cic.Anonymous -> "" | Some (Cic.Name id) -> " we proved " ^ id)
| Case (_, id, args) ->
"case" ^ id ^
String.concat " "