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Proof step 66 from proof addarray-put-01 (previous step)

¬ (r ≠ r ∨ r = r ∧ is_fskey(i ') ∧ i ' ≠ _length ∧ i ' ≠ _type ∨ r = r ∧ is_indexkey(i ') ∧ (i ' .index < 0 ∨ 1 + i0 ≤ i ' .index)), 0 < i0, 0 < i, r -- i ' ∈ addarray(r, ty, val ' + mklist(initial_value(ty), i→n(i0)), st), 0 ≤ i0, i ≤ i0 ⊦ i = 0, r -- i ' ∈ addarray(r, ty, 1 + i0, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 65:
0 < i0, 0 < i, r -- i ' ∈ addarray(r, ty, val ' + mklist(initial_value(ty), i→n(i0)), st), 0 ≤ i0, i ≤ i0 ⊦ i = 0, r -- i ' ∈ addarray(r, ty, 1 + i0, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i + 1 ≤ j ↔ i < j], [CSIMPSEQ : ⊦ i < j → ¬ j < i], [CSIMPSEQ : ⊦ i ' .index = i], [CSIMPSEQ : ⊦ is_indexkey(i ')], [CSIMPSEQ : ⊦ ¬ is_fskey(i ')])]]