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Proof step 10 from proof putArray-in (previous step)

r0 -- sk ∈ putArray(vals0, r, i + 1, st[r -- i ', val]), r0 -- sk ∈ putArray(vals0, r, i + 1, st[r -- i ', val]) ↔ r0 = r ∧ is_indexkey(sk) ∧ i < sk .index ∧ sk .index ≤ i + n→i(# vals0) ∨ r0 -- sk ∈ st[r -- i ', val], ∀ rk, r, i, st. rk ∈ putArray(vals0, r, i, st) ↔ rk ∈ st ∨ rk .ref = r ∧ is_indexkey(rk .key) ∧ i ≤ rk .key .index ∧ rk .key .index < i + n→i(# vals0) ⊦ r0 = r ∧ ¬ is_fskey(sk) ∧ ¬ sk .index < i ∧ ¬ n→i(# vals0) + i < sk .index ∨ r0 -- sk ∈ st

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ r ≠ r0 → (r0 -- sk ∈ putArray(vals, r, j, st) ↔ r0 -- sk ∈ st)
Proof step 9:
r -- sk ∈ putArray(vals0, r, i + 1, st[r -- i ', val]), r ∈ putArray(vals0, r, i + 1, st[r -- i ', val]), sk = i ' ∨ is_indexkey(sk) ∧ i < sk .index ∧ sk .index ≤ i + n→i(# vals0), ∀ rk, r, i, st. rk ∈ putArray(vals0, r, i, st) ↔ rk ∈ st ∨ rk .ref = r ∧ is_indexkey(rk .key) ∧ i ≤ rk .key .index ∧ rk .key .index < i + n→i(# vals0) ⊦ r -- sk ∈ st, ¬ n→i(# vals0) + i < sk .index ∧ ¬ sk .index < i ∧ ¬ is_fskey(sk)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ r ≠ r0 → ( r -- sk ∈ st[r0 -- sk0, val] ↔ r -- sk ∈ st)], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ is_indexkey(sk) ↔ is_fskey(sk)], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st])]]