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Proof step 11 from proof add-put-switch (previous step)

i > 0, is_fskey(sk), ∀ val0, st, val, r0, sk, i0. i→n(i0) < i→n(i) → (is_fskey(sk) → addarray(r0, val, i0, st[r0 -- sk, val0]) = (addarray(r0, val, i0, st)[r0 -- sk, val0])) ⊦ (addarray(r0, val, i - 1, st[r0 -- sk, val0])[r0 -- (i - 1) ', val]) = (addarray(r0, val, i, st)[r0 -- sk, val0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
is_fskey(sk), 0 < i, ∀ val0, st, val, r0, sk, i0. i→n(i0) < i→n(i) → (is_fskey(sk) → addarray(r0, val, i0, st[r0 -- sk, val0]) = (addarray(r0, val, i0, st)[r0 -- sk, val0])) ⊦ (addarray(r0, val, i - 1, st[r0 -- sk, val0])[r0 -- (i - 1) ', val]) = (addarray(r0, val, i, st)[r0 -- sk, val0])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ i > j ↔ j < i])]]