27 lines
1.2 KiB
Text
27 lines
1.2 KiB
Text
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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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Assumed: f
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f (v ; w ; empty ; (v ; empty))
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===>
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f (v ; (w ; v))
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hcongr (hcongr (hrefl @f)
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(to_heq (subst (refl (vec (n + n + 0 + (n + 0))))
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(congr2 vec
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(trans (congr (congr2 Nat::add (Nat::add_zeror (n + n))) (Nat::add_zeror n))
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(Nat::add_assoc n n n))))))
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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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