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Proof step 7 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, r, 0, addarray(r, initial_value(ty), n→i(# vals1), st))[r -- n→i(# vals1) ', val]) = (addarray(r, vals1, 0, st)[r -- n→i(# vals1) ', val])

User applied rule apply induction

And closed the goal!

Rule argument

[substlist-arg: [st, ty, r, vals0] → [st, ty, r, vals1]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # (vals + vals0) = # vals + # vals0], [CSIMPSEQ : ⊦ # val ' = 0 +1], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ m < n + 1 ↔ ¬ n < m], [CSIMPSEQ : ⊦ ¬ n < n], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (st, ty, r, vals1)]]