equal
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inserted
replaced
44 Locales are based on contexts. A \emph{context} can be seen as a |
44 Locales are based on contexts. A \emph{context} can be seen as a |
45 formula schema |
45 formula schema |
46 \[ |
46 \[ |
47 \isa{{\isasymAnd}x\isactrlsub {\isadigit{1}}{\isasymdots}x\isactrlsub n{\isachardot}\ {\isasymlbrakk}\ A\isactrlsub {\isadigit{1}}{\isacharsemicolon}\ {\isasymdots}\ {\isacharsemicolon}A\isactrlsub m\ {\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isasymdots}} |
47 \isa{{\isasymAnd}x\isactrlsub {\isadigit{1}}{\isasymdots}x\isactrlsub n{\isachardot}\ {\isasymlbrakk}\ A\isactrlsub {\isadigit{1}}{\isacharsemicolon}\ {\isasymdots}\ {\isacharsemicolon}A\isactrlsub m\ {\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isasymdots}} |
48 \] |
48 \] |
49 where variables~\isa{x\isactrlsub {\isadigit{1}}}, \ldots,~\isa{x\isactrlsub n} are called |
49 where the variables~\isa{x\isactrlsub {\isadigit{1}}}, \ldots,~\isa{x\isactrlsub n} are called |
50 \emph{parameters} and the premises $\isa{A\isactrlsub {\isadigit{1}}}, \ldots,~\isa{A\isactrlsub m}$ \emph{assumptions}. A formula~\isa{C} |
50 \emph{parameters} and the premises $\isa{A\isactrlsub {\isadigit{1}}}, \ldots,~\isa{A\isactrlsub m}$ \emph{assumptions}. A formula~\isa{C} |
51 is a \emph{theorem} in the context if it is a conclusion |
51 is a \emph{theorem} in the context if it is a conclusion |
52 \[ |
52 \[ |
53 \isa{{\isasymAnd}x\isactrlsub {\isadigit{1}}{\isasymdots}x\isactrlsub n{\isachardot}\ {\isasymlbrakk}\ A\isactrlsub {\isadigit{1}}{\isacharsemicolon}\ {\isasymdots}\ {\isacharsemicolon}A\isactrlsub m\ {\isasymrbrakk}\ {\isasymLongrightarrow}\ C}. |
53 \isa{{\isasymAnd}x\isactrlsub {\isadigit{1}}{\isasymdots}x\isactrlsub n{\isachardot}\ {\isasymlbrakk}\ A\isactrlsub {\isadigit{1}}{\isacharsemicolon}\ {\isasymdots}\ {\isacharsemicolon}A\isactrlsub m\ {\isasymrbrakk}\ {\isasymLongrightarrow}\ C}. |
54 \] |
54 \] |