refactor

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diff --git a/src/assets/writeup/proof.md b/src/assets/writeup/proof.md
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----
-name: Brainfucked
-desc: trimills turing completeness proof for brainfucked
----
-
-### Turing-completeness proof for Brainfucked
-
-By producing an algorithm that can translate arbitrary Brainfuck programs into
-Brainfucked, we prove that the latter must have computational class greater than
-or equal to the former, thus proving that Brainfucked is Turing-complete.
-
-Proof that Brainfucked is not of a greater computational class than Brainfuck is
-left as an exercise to the reader.
-
-Since Brainfucked tapes have a limited amount of memory, we will implement a
-tape as a linked list. Each item in the linked list will be a tape of length
-ten with the following structure:
-
-- The first cell contains the item's value
-- The second cell is 1 if the next item has already been allocated and 0 otherwise
-- The remaining 8 cells are the pointer to the next item
-
-The second byte is not strictly necessary, as we could just check whether the pointer
-is null, however it makes the translation significantly easier.
-
-First, we prefix the output program with `++++++++++*(`. Since the original tape is
-only 8 bytes wide, we need to make a new one with a size of 10. `+`, `-`, `[`, `]`,
-`.`, and `,` all translate to themselves.
-
-`>` can be translated as `>-[>++++++++++*<+]+>(`. This will allocate the next tape
-if it does not yet exist and then enter it.
-
-First, consider the case where next tape has not yet been allocated. We decrement the
-allocation marker cell, which wraps around to 255, allowing us to enter the loop. We
-then allocate the next tape and increment the allocation marker back to 0. After exiting
-the loop, it is incremented again to 1, signalling that the next tape is now allocated.
-We can then enter the newly allocated tape. If the tape was already allocated, the loop
-will never be entered and the marker will remain 1.
-
-`<` can be translated as `)<<`. We exit the current tape and move back over to the data cell.
-
-This proof only uses a subset of Brainfucked consisting of the characters `+-<>[]()*,.`.
-One of `+` or `-` can be trivially eliminated by replacing it with 255 copies of the other.
-Additionally, `,` and `.` are not required for Turing-completeness, as input can be encoded into
-the initial tape configuration and output can be read off the tape once the program halts.
-I conjecture that no smaller subset of Brainfucked is Turing-complete.
-
-#### Example translation script (Lua)
-```lua
-src = io.read("*a")
-src = src:gsub("%<", ")<<")
-src = src:gsub("%>", ">-[>++++++++++*<+]+>(")
-src = "++++++++++*(" .. src
-io.write(src)
-```