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Proof step 11 from proof putarray-add-same-02 (previous step)

∀ st, ty, r, vals0. # vals0 < # (vals1 + val ') → (true → putArray(vals0, r, 0, addarray(r, initial_value(ty), n→i(# vals0), st)) = addarray(r, vals0, 0, st)) ⊦ putArray(vals1 + val ', r, 0, addarray(r, initial_value(ty), n→i(# vals1), st)[r -- n→i(# vals1) ', initial_value(ty)]) = (addarray(r, vals1, 0, st)[r -- n→i(# vals1) ', val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ putArray(vals + val ', r, i, st) = putArray(vals, r, i, st[r -- (i + n→i(# vals)) ', val])
Proof step 10:
∀ st, ty, r, vals0. # vals0 < # (vals1 + val ') → (true → putArray(vals0, r, 0, addarray(r, initial_value(ty), n→i(# vals0), st)) = addarray(r, vals0, 0, st)) ⊦ putArray(vals1, r, 0, addarray(r, initial_value(ty), n→i(# vals1), st)[r -- n→i(# vals1) ', initial_value(ty)][r -- (0 + n→i(# vals1)) ', val]) = (addarray(r, vals1, 0, st)[r -- n→i(# vals1) ', val])

Rule argument

[speclemmaarg: , putArray(vals + val ', r, i, st) = putArray(vals, r, i, st[r -- (i + n→i(# vals)) ', val]) ,[st, i, r, val, vals] → [addarray(r, initial_value(ty), n→i(# vals1), st) [r -- n→i(# vals1) ', initial_value(ty) ], 0, r, val, vals1] ,F ,storearrays , ,putAr-lastrec ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (addarray(r, initial_value(ty), n→i(# vals1), st) [r -- n→i(# vals1) ', initial_value(ty) ], 0, r, val, vals1)]]