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Proof step 5 from proof putArray-put-switch-01 (previous step)

r0 -- fs ' ≠ r -- i ', ∀ 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)[r0 -- fs ', val][r -- i ', val0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
∀ 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)[r0 -- fs ', val][r -- i ', val0])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ fs ' ≠ i '], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)])]]