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Proof step 28 from proof get-alleq (previous step)

∀ j0, r, i, st, r0, i0, st0. i→n(j0) < i→n(j) → (true → (getarray(r, i, j0, st) = getarray(r0, i0, j0, st0) ↔ (∀ j1. 0 ≤ j1 ∧ j1 < j0 → st[r -- (i + j1) '] = st0[r0 -- (i0 + j1) ']))) ⊦ getarray(r, i, j, st) = getarray(r0, i0, j, st0) ↔ (∀ j0. 0 ≤ j0 ∧ j0 < j → st[r -- (i + j0) '] = st0[r0 -- (i0 + j0) '])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ 1 < j → getarray(r, i, j, st) = getarray(r, i, j - 1, st) + st[r -- (i + j - 1) ']
Proof step 10:
¬ 1 < j, ∀ j0, r, i, st, r0, i0, st0. i→n(j0) < i→n(j) → (true → (getarray(r, i, j0, st) = getarray(r0, i0, j0, st0) ↔ (∀ j1. 0 ≤ j1 ∧ j1 < j0 → st[r -- (i + j1) '] = st0[r0 -- (i0 + j1) ']))) ⊦ getarray(r, i, j, st) = getarray(r0, i0, j, st0) ↔ (∀ j0. 0 ≤ j0 ∧ j0 < j → st[r -- (i + j0) '] = st0[r0 -- (i0 + j0) '])
Proof step 27:
1 < j, ∀ j0, r, i, st, r0, i0, st0. i→n(j0) < i→n(j) → (true → (getarray(r, i, j0, st) = getarray(r0, i0, j0, st0) ↔ (∀ j1. 0 ≤ j1 ∧ j1 < j0 → st[r -- (i + j1) '] = st0[r0 -- (i0 + j1) ']))) ⊦ getarray(r, i, j - 1, st) + st[r -- (i + j - 1) '] = getarray(r0, i0, j, st0) ↔ (∀ j0. 0 ≤ j0 ∧ j0 < j → st[r -- (i + j0) '] = st0[r0 -- (i0 + j0) '])

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, j, i, r)]]