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Proof step 49 from proof addarray-addaray (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
⊦ rk ∈ st → rk ∈ addarray(r, ty, vals, st)
Proof step 43:
⊦ r ∈ addarray(r, ty0, vals, st)
Proof step 48:
r -- sk ∈ addarray(r, ty, mklist(initial_value(ty), i→n(i)), st), 0 ≤ i, is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type ∨ is_indexkey(sk) ∧ (sk .index < 0 ∨ i ≤ sk .index) ⊦ r -- sk ∈ st

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st])]]