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Proof step 12 from proof putarray-add-same-02 (previous step)

vals = vals1 + val ', n→i(# vals) = i + 1, ∀ st, ty, r, vals0. # vals0 < # vals → (true → putArray(vals0, r, 0, addarray(r, initial_value(ty), n→i(# vals0), st)) = addarray(r, vals0, 0, st)) ⊦ vals = [], putArray(vals, r, 0, addarray(r, initial_value(ty), i, st)[r -- i ', initial_value(ty)]) = (addarray(r, vals1, 0, st)[r -- i ', val])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
∀ 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])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ vals + val ' ≠ []], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = i + i0 ↔ j = i0], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ # val ' = 0 +1], [CSIMPSEQ : ⊦ # (vals + vals0) = # vals + # vals0])]]