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List.lp

Lines changed: 30 additions & 30 deletions
Original file line numberDiff line numberDiff 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 (lm) = rev mrev l) ≔
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begin
91-
assume a;
92-
induction;
93-
// case l = □
94-
simplify;
95-
assume x;
96-
reflexivity;
97-
// case l = ⸬
98-
assume x l' hl' m;
99-
simplify;
100-
rewrite hl';
101-
reflexivity;
91+
assume a;
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induction;
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// case l = □
94+
simplify;
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assume x;
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reflexivity;
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// case l = ⸬
98+
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 $mrev $l;
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opaque symbol rev_idem {a} (l :𝕃 a) : π(rev (rev l) = l) ≔
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begin
108-
assume a;
109-
induction;
110-
// case l = □
111-
reflexivity;
112-
// case l = ⸬
113-
assume x l' hl';
114-
simplify;
115-
rewrite hl';
116-
reflexivity;
108+
assume a;
109+
induction;
110+
// case l = □
111+
reflexivity;
112+
// case l = ⸬
113+
assume x l' hl';
114+
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
123-
assume a;
124-
induction;
125-
// case l = □
126-
simplify;
127-
reflexivity;
128-
// case l = ⸬
129-
assume x l' hl';
130-
simplify;
131-
rewrite hl';
132-
reflexivity;
123+
assume a;
124+
induction;
125+
// case l = □
126+
simplify;
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reflexivity;
128+
// case l = ⸬
129+
assume x l' hl';
130+
simplify;
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rewrite hl';
132+
reflexivity;
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end;
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rule length (rev $l) ↪ length $l;

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