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Proof step 9 from proof putar-in-02 (previous step)

∀ r, j, i, st. r -- j ' ∈ putArray(vals0, r, i, st) ↔ ¬ j < i ∧ ¬ i + n→i(# vals0) ≤ j ∨ r -- j ' ∈ st ⊦ r -- j ' ∈ putArray(val + vals0, r, i, st) ↔ ¬ j < i ∧ ¬ i + n→i(# (val + vals0)) ≤ j ∨ r -- j ' ∈ st

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ putArray(val ' + vals, r, i, st) = (putArray(vals, r, i + 1, st)[r -- i ', val])
Proof step 8:
∀ r0, j0, i0, st0. r0 -- j0 ' ∈ putArray(vals0, r0, i0, st0) ↔ r0 -- j0 ' ∈ st0 ∨ i0 ≤ j0 ∧ j0 < i0 + n→i(# vals0) ⊦ r -- j ' ∈ (putArray(vals0, r, i + 1, st)[r -- i ', val]) ↔ r -- j ' ∈ st ∨ ¬ n→i(# vals0) + i < j ∧ ¬ j < i

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + 1 ≤ j ↔ i < j], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ # val ' = 0 +1], [CSIMPSEQ : ⊦ # (vals + vals0) = # vals + # vals0], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ val + vals = val ' + vals])]]