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Proof step 7 from proof putArray-put-switch-01 (previous step)

∀ r, i, st, r0, fs, val. putArray(vals0, r, i, st[r0 -- fs ', val]) = (putArray(vals0, r, i, st)[r0 -- fs ', val]) ⊦ putArray(val0 + vals0, r, i, st[r0 -- fs ', val]) = (putArray(val0 + vals0, r, i, st)[r0 -- fs ', val])

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 6:
∀ r, i, st, r0, fs, val. putArray(vals0, r, i, st[r0 -- fs ', val]) = (putArray(vals0, r, i, st)[r0 -- fs ', val]) ⊦ (putArray(vals0, r, i + 1, st[r0 -- fs ', val])[r -- i ', val0]) = (putArray(vals0, r, i + 1, st)[r -- i ', val0][r0 -- fs ', val])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ val + vals = val ' + vals])]]