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Proof step 9 from proof get-alleq (previous step)

j ≤ 1, ∀ 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 2:
⊦ j ≤ 0 → getarray(r, i, j, st) = []
Proof step 7:
¬ j ≤ 0, j ≤ 1, ∀ 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 8:
⊦ j ≤ 0 → getarray(r, i, j, st) = []

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : j0 ≠ 0, j ≤ j0 ⊦ i ≤ ((* j)) → i ≤ ((* j0))], [CSIMPFORWARD : ⊦ i < j ∧ j ≤ j0 → i < j0], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1], [CSIMPFORWARD : ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])], [EXTRATERMS : (st, j, i, r)]]