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lines changed Original file line number Diff line number Diff line change @@ -88,48 +88,48 @@ with rev ($x ⸬ $l) ↪ rev $l ⋅ ($x ⸬ □);
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opaque symbol rev_concat {a } (l m : 𝕃 a ) : π(rev (l ⋅ m ) = rev m ⋅ rev l ) ≔
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begin
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- assume a ;
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- induction ;
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- // case l = □
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- simplify ;
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- assume x ;
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- reflexivity ;
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- // case l = ⸬
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- assume x l ' hl ' m ;
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- simplify ;
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- rewrite hl ';
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- reflexivity ;
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+ assume a ;
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+ induction ;
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+ // case l = □
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+ simplify ;
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+ assume x ;
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+ reflexivity ;
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+ // case l = ⸬
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+ assume x l ' hl ' m ;
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+ simplify ;
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+ rewrite hl ';
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+ reflexivity ;
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end ;
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rule rev ($l ⋅ $m ) ↪ rev $m ⋅ rev $l ;
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opaque symbol rev_idem {a } (l :𝕃 a ) : π(rev (rev l ) = l ) ≔
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begin
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- assume a ;
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- induction ;
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- // case l = □
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- reflexivity ;
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- // case l = ⸬
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- assume x l ' hl ';
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- simplify ;
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- rewrite hl ';
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- reflexivity ;
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+ assume a ;
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+ induction ;
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+ // case l = □
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+ reflexivity ;
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+ // case l = ⸬
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+ assume x l ' hl ';
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+ simplify ;
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+ rewrite hl ';
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+ reflexivity ;
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end ;
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rule rev (rev $l ) ↪ $l ;
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opaque symbol length_rev {a } (l : 𝕃 a ) : π(length (rev l ) = length l ) ≔
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begin
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- assume a ;
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- induction ;
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- // case l = □
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- simplify ;
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- reflexivity ;
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- // case l = ⸬
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- assume x l ' hl ';
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- simplify ;
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- rewrite hl ';
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- reflexivity ;
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+ assume a ;
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+ induction ;
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+ // case l = □
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+ simplify ;
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+ reflexivity ;
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+ // case l = ⸬
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+ assume x l ' hl ';
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+ simplify ;
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+ rewrite hl ';
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+ reflexivity ;
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end ;
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rule length (rev $l ) ↪ length $l ;
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