20 lines
793 B
Text
20 lines
793 B
Text
Set: pp::colors
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Set: pp::unicode
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Assumed: vec
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Assumed: concat
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Assumed: concat_assoc
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Assumed: empty
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Assumed: concat_empty
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Assumed: n
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Assumed: v
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Assumed: w
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v ; w ; empty ; (v ; empty)
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===>
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v ; (w ; v)
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htrans (htrans (hcongr (hcongr (hcongr (hcongr (hrefl @concat) (to_heq (Nat::add_zeror (n + n))))
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(to_heq (Nat::add_zeror n)))
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(htrans (to_heq (concat_empty (v ; w)))
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(cast_heq (congr2 vec (symm (Nat::add_zeror (n + n)))) (v ; w))))
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(htrans (to_heq (concat_empty v)) (cast_heq (congr2 vec (symm (Nat::add_zeror n))) v)))
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(to_heq (concat_assoc v w v)))
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(cast_heq (congr2 vec (symm (Nat::add_assoc n n n))) (v ; (w ; v)))
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