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Proof step 30 from proof putBar-rew (previous step)

j < i ∨ i + n→i(# bytes) ≤ j ⊦ ∀ rk. (rk ∈ (putByteArray(bytes, r, i, st)[r -- j ', val]) ↔ rk ∈ putByteArray(bytes, r, i, st[r -- j ', val])) ∧ (putByteArray(bytes, r, i, st)[r -- j ', val][rk]) = (putByteArray(bytes, r, i, st[r -- j ', val])[rk])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ rk ∈ putByteArray(bytes, r, i, st) ↔ rk ∈ st ∨ rk .ref = r ∧ is_indexkey(rk .key) ∧ i ≤ rk .key .index ∧ rk .key .index < i + n→i(# bytes)
Proof step 29:
j < i ∨ i + n→i(# bytes) ≤ j ⊦ ((rk = r -- j ' ⊃ val; putByteArray(bytes, r, i, st)[rk])) = (putByteArray(bytes, r, i, st[r -- j ', val])[rk])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ is_indexkey(sk) → ¬ is_fskey(sk)], [CSIMPSEQ : ⊦ (st[rk0, val][rk]) = ((rk = rk0 ⊃ val; st[rk]))], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ¬ is_indexkey(sk) ↔ is_fskey(sk)], [CSIMPSEQ : ⊦ rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st])]]