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Proof step 7 from proof add-put-switch (previous step)

r0 -- sk ≠ r0 -- i1 ', is_fskey(sk), 0 ≤ i1, ∀ val0, st, val, r0, sk, i0. i→n(i0) < i→n(i1 + 1) → (is_fskey(sk) → addarray(r0, val, i0, st[r0 -- sk, val0]) = (addarray(r0, val, i0, st)[r0 -- sk, val0])) ⊦ (addarray(r0, val, i1, st[r0 -- sk, val0])[r0 -- i1 ', val]) = (addarray(r0, val, i1, st)[r0 -- sk, val0][r0 -- i1 ', val])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
is_fskey(sk), 0 ≤ i1, ∀ val0, st, val, r0, sk, i0. i→n(i0) < i→n(i1 + 1) → (is_fskey(sk) → addarray(r0, val, i0, st[r0 -- sk, val0]) = (addarray(r0, val, i0, st)[r0 -- sk, val0])) ⊦ (addarray(r0, val, i1, st[r0 -- sk, val0])[r0 -- i1 ', val]) = (addarray(r0, val, i1, st)[r0 -- sk, val0][r0 -- i1 ', val]), sk = i1 '

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)])]]