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Proof step 4 from proof putArray-append (previous step)

∀ vals0, r, i, st. putArray(vals1 + vals0, r, i, st) = putArray(vals1, r, i, putArray(vals0, r, i + n→i(# vals1), st)) ⊦ putArray((val + vals1) + vals0, r, i, st) = putArray(val + vals1, r, i, putArray(vals0, r, i + n→i(# (val + vals1)), st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ putArray(val ' + vals, r, i, st) = (putArray(vals, r, i + 1, st)[r -- i ', val])
Proof step 3:
∀ vals0, r, i, st. putArray(vals1 + vals0, r, i, st) = putArray(vals1, r, i, putArray(vals0, r, i + n→i(# vals1), st)) ⊦ (putArray(vals1 + vals0, r, i + 1, st)[r -- i ', val]) = (putArray(vals1, r, i + 1, putArray(vals0, r, (1 + n→i(# vals1)) + i, st))[r -- i ', val])

Rule argument

[emptyarg]

Additional information

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