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Proof step 17 from proof isarray-put-samefield-01 (conclusion)

⊦ r -- fs ' ∈ st ∧ oktype(st[r -- fs '], fs .type, st) ∧ oktype(val, fs .type, st) ∧ fs ' ≠ _type ∧ fs ' ≠ _length → (is_array(r, st[r -- fs ', val]) ↔ is_array(r, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 1:
⊦ is_array(r, st) ∧ oktype(val, fs .type, st) ∧ fs ' ≠ _type ∧ fs ' ≠ _length → is_array(r, st[r -- fs ', val])
Proof step 16:
r -- fs ' ∈ st, oktype(st[r -- fs '], fs .type, st), oktype(val, fs .type, st), is_array(r, st[r -- fs ', val]), r ∈ st ⊦ fs ' = _length, fs ' = _type, is_array(r, st)

Rule argument

[emptyarg]

Additional information

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