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61 lines
2.5 KiB
Plaintext
61 lines
2.5 KiB
Plaintext
concrete LogicEng of Logic = open LogicResEng, Prelude in {
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flags lexer=vars ; unlexer=text ;
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lincat
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Dom = {s : Num => Str} ;
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Prop, Elem = {s : Str} ;
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lin
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Statement A = {s = A.s ++ "."} ;
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ThmWithProof A a = {s =
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["Theorem ."] ++ A.s ++ "." ++ PARA ++ "Proof" ++ "." ++ a.s ++ "."} ;
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ThmWithTrivialProof A a =
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{s = "Theorem" ++ "." ++ A.s ++ "." ++ PARA ++ "Proof" ++ "." ++ "Trivial" ++ "."} ;
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Disj A B = {s = A.s ++ "or" ++ B.s} ;
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Conj A B = {s = A.s ++ "and" ++ B.s} ;
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Impl A B = {s = "if" ++ A.s ++ "then" ++ B.s} ;
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Univ A B = {s = ["for all"] ++ A.s ! pl ++ B.$0 ++ "," ++ B.s} ;
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Exist A B =
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{s = ["there exists"] ++ indef ++ A.s ! sg ++ B.$0 ++ ["such that"] ++ B.s} ;
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Abs = {s = ["we have a contradiction"]} ;
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Neg A = {s = ["it is not the case that"] ++ A.s} ;
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ImplP A B = {s = "if" ++ A.s ++ "then" ++ B.s} ;
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ConjI A B a b = {s = a.s ++ "." ++ b.s ++ [". Hence"] ++ A.s ++ "and" ++ B.s} ;
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ConjEl A B c = {s = c.s ++ [". A fortiori ,"] ++ A.s} ;
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ConjEr A B c = {s = c.s ++ [". A fortiori ,"] ++ B.s} ;
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DisjIl A B a = {s = a.s ++ [". A fortiori ,"] ++ A.s ++ "or" ++ B.s} ;
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DisjIr A B b = {s = b.s ++ [". A fortiori ,"] ++ A.s ++ "or" ++ B.s} ;
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DisjE A B C c d e = {s =
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c.s ++
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[". There are two possibilities . First , assume"] ++
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A.s ++ "(" ++ d.$0 ++ ")" ++ "." ++ d.s ++
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[". Second , assume"] ++ B.s ++ "(" ++ e.$0 ++ ")" ++ "." ++ e.s ++
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[". Thus"] ++ C.s ++ ["in both cases"]} ;
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ImplI A B b = {s =
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"assume" ++ A.s ++ "(" ++ b.$0 ++ ")" ++ "." ++
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b.s ++ [". Hence , if"] ++ A.s ++ "then" ++ B.s} ;
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ImplE A B c a = {s = a.s ++ [". But"] ++ c.s ++ [". Hence"] ++ B.s} ;
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NegI A b = {s =
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"assume" ++ A.s ++ "(" ++ b.$0 ++ ")" ++ "." ++ b.s ++
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[". Hence, it is not the case that"] ++ A.s} ;
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NegE A c a =
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{s = a.s ++ [". But"] ++ c.s ++ [". We have a contradiction"]} ;
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UnivI A B b = {s =
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["consider an arbitrary"] ++ A.s ! sg ++ b.$0 ++ "." ++ b.s ++
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[". Hence, for all"] ++ A.s ! pl ++ B.$0 ++ "," ++ B.s} ;
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UnivE A B c a =
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{s = c.s ++ [". Hence"] ++ B.s ++ "for" ++ B.$0 ++ ["set to"] ++ a.s} ;
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ExistI A B a b = {s =
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b.s ++ [". Hence, there exists"] ++ indef ++
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A.s ! sg ++ B.$0 ++ ["such that"] ++ B.s} ;
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ExistE A B C c d = {s =
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c.s ++ [". Consider an arbitrary"] ++ d.$0 ++
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["and assume that"] ++ B.s ++ "(" ++ d.$1 ++ ")" ++ "." ++ d.s ++
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[". Hence"] ++ C.s ++ ["independently of"] ++ d.$0} ;
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AbsE C c = {s = c.s ++ [". We may conclude"] ++ C.s} ;
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Hypo A a = {s = ["by the hypothesis"] ++ a.s ++ "," ++ A.s} ;
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Pron _ _ = {s = "it"} ;
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} ;
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