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Proof step 20 from proof putAr-lastrec (previous step)

putArray(vals0 + val ', r, i + 1, st[r -- i ', val0]) = (putArray(vals0, r, i + 1, st)[r -- ((i + 1) + n→i(# vals0)) ', val][r -- i ', val0]), ∀ val, r, i, st. putArray(vals0 + val ', r, i, st) = (putArray(vals0, r, i, st)[r -- (i + n→i(# vals0)) ', val]) ⊦ (putArray(vals0 + val ', r, i + 1, st)[r -- i ', val0]) = (putArray(vals0, r, i + 1, st)[r -- ((i + 1) + n→i(# vals0)) ', val][r -- i ', val0])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ rk .ref ≠ r ∨ is_fskey(rk .key) ∨ rk .key .index < j ∨ n→i(# vals) + j ≤ rk .key .index → (putArray(vals, r, j, st)[rk, val]) = putArray(vals, r, j, st[rk, val])

Rule argument

[crewrite-arg: putar-rew , F , [val, rk, st, j, r, vals] → [val0, r -- i ', st, i + 1, r, vals0 + val '] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r -- sk) .ref = r], [CSIMPSEQ : ⊦ (r -- sk) .key = sk], [CSIMPSEQ : ⊦ ¬ is_fskey(i ')], [CSIMPSEQ : ⊦ i ' .index = i], [CSIMPSEQ : ⊦ i < j + 1 ↔ i ≤ j], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ¬ i < i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (val0, r -- i ', st, i + 1, r, vals0 + val ')]]