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Proof step 10 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) ', initial_value(ty)][r -- (0 + n→i(# vals1)) ', val]) = (addarray(r, vals1, 0, st)[r -- n→i(# vals1) ', val])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
∀ 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])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (st[rk, val][rk, val0]) = st[rk, val0]], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + 0 = i])]]