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Proof step 14 from proof putar-getar-01 (previous step)

∀ r, r0, i, j, st. r = r0 ∨ getarray(r, i, j, putArray(vals0, r0, i, st)) = getarray(r, i, j, st) ⊦ r = r0, getarray(r, i, j, putArray(vals0, r0, i + 1, st)[r0 -- i ', val]) = getarray(r, i, j, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 < j → getarray(r, i, j, st) = st[r -- i '] ' + getarray(r, i + 1, j - 1, st)
Proof step 4:
⊦ j ≤ 0 → getarray(r, i, j, st) = []
Proof step 13:
0 < j, ∀ r, r0, i, j, st. r = r0 ∨ getarray(r, i, j, putArray(vals0, r0, i, st)) = getarray(r, i, j, st) ⊦ r = r0, (putArray(vals0, r0, i + 1, st)[r0 -- i ', val][r -- i ']) ' + getarray(r, i + 1, j - 1, putArray(vals0, r0, i + 1, st)[r0 -- i ', val]) = getarray(r, i, j, st)

Rule argument

[crewrite-arg: get-rec-01 , F , [st, j, i, r] → [putArray(vals0, r0, i + 1, st)[r0 -- i ', val], j, i, r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i])], [EXTRATERMS : (putArray(vals0, r0, i + 1, st)[r0 -- i ', val], j, i, r)]]