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Proof step 9 from proof add-at-05 (previous step)

i > 0, is_fskey(sk), ∀ r0, st, val, r, sk, i0. i→n(i0) < i→n(i) → (is_fskey(sk) → (addarray(r, val, i0, st)[r0 -- sk]) = st[r0 -- sk]) ⊦ (addarray(r, val, i - 1, st)[r -- (i - 1) ', val][r0 -- sk]) = st[r0 -- sk]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
is_fskey(sk), 0 < i, ∀ r0, st, val, r, sk, i0. i→n(i0) < i→n(i) → (is_fskey(sk) → (addarray(r, val, i0, st)[r0 -- sk]) = st[r0 -- sk]) ⊦ (((r0 = r ∧ sk = (i - 1) ') ⊃ val; addarray(r, val, i - 1, st)[r0 -- sk])) = st[r0 -- sk]

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ i > j ↔ j < i], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ (st[rk0, val][rk]) = ((rk = rk0 ⊃ val; st[rk]))])]]