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Proof step 21 from proof Comp-get-01 (previous step)

∀ i. ¬ i < 0 ∧ ¬ j ≤ i → st[r1 -- (i1 + i) '] = st[r2 -- (i2 + i) '], ∀ j0, st, r1, i1, r2, i2. i→n(j0) < i→n(j) → ((∀ i. ¬ i < 0 ∧ ¬ j0 ≤ i → st[r1 -- (i1 + i) '] = st[r2 -- (i2 + i) ']) → getarray(r1, i1, j0, st) = getarray(r2, i2, j0, st)) ⊦ getarray(r1, i1, j, st) = getarray(r2, i2, j, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ 1 < j → getarray(r, i, j, st) = getarray(r, i, j - 1, st) + st[r -- (i + j - 1) ']
Proof step 9:
¬ 1 < j, ∀ i. ¬ i < 0 ∧ ¬ j ≤ i → st[r1 -- (i1 + i) '] = st[r2 -- (i2 + i) '], ∀ j0, st, r1, i1, r2, i2. i→n(j0) < i→n(j) → ((∀ i. ¬ i < 0 ∧ ¬ j0 ≤ i → st[r1 -- (i1 + i) '] = st[r2 -- (i2 + i) ']) → getarray(r1, i1, j0, st) = getarray(r2, i2, j0, st)) ⊦ getarray(r1, i1, j, st) = getarray(r2, i2, j, st)
Proof step 20:
1 < j, ∀ i. ¬ i < 0 ∧ ¬ j ≤ i → st[r1 -- (i1 + i) '] = st[r2 -- (i2 + i) '], ∀ j0, st, r1, i1, r2, i2. i→n(j0) < i→n(j) → ((∀ i. ¬ i < 0 ∧ ¬ j0 ≤ i → st[r1 -- (i1 + i) '] = st[r2 -- (i2 + i) ']) → getarray(r1, i1, j0, st) = getarray(r2, i2, j0, st)) ⊦ getarray(r1, i1, j - 1, st) + st[r1 -- (i1 + j - 1) '] = getarray(r2, i2, j, st)

Rule argument

[crewrite-arg: getArray-rec, F, [st, j, i, r] → [st, j, i1, r1]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, j, i1, r1)]]