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Proof step 11 from proof putarray-add-same (previous step)

¬ (r ≠ r0 ∨ r = r0 ∧ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type ∨ r = r0 ∧ is_indexkey(sk) ∧ (sk .index < 0 ∨ n→i(# vals) ≤ sk .index)) ⊦ r0 -- sk ∈ addarray(r, ty, n→i(# vals), st) ∨ r0 = r ∧ is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < n→i(# vals) ↔ r0 -- sk ∈ addarray(r, ty, vals, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
⊦ r -- _length ∈ addarray(r, ty, i, st)
Proof step 6:
⊦ r -- _length ∈ addarray(r, ty, vals, st)
Proof step 7:
⊦ r -- _type ∈ addarray(r, ty, i, st)
Proof step 8:
⊦ r -- _type ∈ addarray(r, ty, vals, st)
Proof step 10:
0 ≤ sk .index, sk .index < n→i(# vals), is_indexkey(sk) ⊦ sk = _length, sk = _type, vals = [], r0 -- sk ∈ addarray(r0, ty, vals, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # vals = 0 ↔ vals = []], [CSIMPSEQ : ⊦ 0 < n ↔ n ≠ 0], [CSIMPSEQ : 0 ≤ i ⊦ ((* i)) < n→i(n) ↔ i→n(i) < n], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ is_indexkey(sk) → ¬ is_fskey(sk)], [CSIMPSEQ : ⊦ ¬ is_indexkey(sk) ↔ is_fskey(sk)], [CSIMPSEQ : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)])]]