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Proof step 9 from proof init-switch (previous step)

r0 -- sk ≠ r -- i ', is_fskey(sk), ∀ sk0, r1, i0, st0, r2, val1. ¬ is_indexkey(sk0) → addarray(r1, vals0, i0, st0[r2 -- sk0, val1]) = (addarray(r1, vals0, i0, st0)[r2 -- sk0, val1]) ⊦ (addarray(r, vals0, i + 1, st[r0 -- sk, val0])[r -- i ', val]) = (addarray(r, vals0, i + 1, st)[r0 -- sk, val0][r -- i ', val])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ r ≠ r0 → (addarray(r, vals, j, st)[r0 -- sk, val]) = addarray(r, vals, j, st[r0 -- sk, val])
Proof step 8:
is_fskey(sk), ∀ sk0, r1, i0, st0, r2, val1. ¬ is_indexkey(sk0) → addarray(r1, vals0, i0, st0[r2 -- sk0, val1]) = (addarray(r1, vals0, i0, st0)[r2 -- sk0, val1]) ⊦ sk = i ', (addarray(r, vals0, i + 1, st[r -- sk, val0])[r -- i ', val]) = (addarray(r, vals0, i + 1, st)[r -- sk, val0][r -- i ', val])

Rule argument

[emptyarg]

Additional information

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