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Proof step 7 from proof newref-1dim-01 (previous step)

0 < i, ∀ st, val, r, r0, i0. i→n(i0) < i→n(i) → (0 < i0 → (newref(r0, addarray(r, val, i0, st)) ↔ r ≠ r0 ∧ newref(r0, st))) ⊦ newref(r0, addarray(r, val, i, st)) ↔ r ≠ r0 ∧ newref(r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ i > 0 → addarray(r, val, i, st) = (addarray(r, val, i - 1, st)[r -- (i - 1) ', val])
Proof step 6:
i > 0, 0 < i, ∀ st, val, r, r0, i0. i→n(i0) < i→n(i) → (0 < i0 → (newref(r0, addarray(r, val, i0, st)) ↔ r ≠ r0 ∧ newref(r0, st))) ⊦ newref(r0, addarray(r, val, i - 1, st)[r -- (i - 1) ', val]) ↔ r ≠ r0 ∧ newref(r0, st)

Rule argument

[crewrite-arg: addarray-rec, F, [st, i, val, r] → [st, i, val, r]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i > j ↔ j < i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (st, i, val, r)]]