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Proof step 18 from proof is_valid_ref-put-samefield (conclusion)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 1:
⊦ is_valid_ref(str, r, st) ↔ ¬ ¬ (is_valid_ref(r, st) ∧ (is_obj(str, r, st) ∨ is_array(str, r, st)))
Proof step 2:
⊦ r -- fs ' ∈ st ∧ oktype(st[r -- fs '], fs .type, st) ∧ oktype(val, fs .type, st) ∧ fs ' ≠ _length ∧ fs ' ≠ _type → (is_valid_ref(r, st[r -- fs ', val]) ↔ is_valid_ref(r, st))
Proof step 3:
⊦ is_obj(str, r, st) ↔ class+∃(str, st[r -- _type] .type .class) ∧ ¬ is_abstract(st[r -- _type] .type .class) ∧ is_obj(r, st)
Proof step 4:
⊦ r -- fs ' ∈ st ∧ oktype(st[r -- fs '], fs .type, st) ∧ oktype(val, fs .type, st) ∧ fs ' ≠ _type → (is_obj(r, st[r -- fs ', val]) ↔ is_obj(r, st))
Proof step 5:
⊦ is_valid_ref(str, r, st) ↔ is_obj(str, r, st) ∨ is_array(str, r, st)
Proof step 6:
⊦ is_obj(r, st) → is_valid_ref(r, st)
Proof step 17:
class+∃(str, st[r -- _type] .type .class), is_obj(r, st), r -- fs ' ∈ st, okval(st[r -- fs '], fs .type), okval(val, fs .type), r ∈ st ⊦ fs ' = _type, fs ' = _length, is_obj(str, r, st[r -- fs ', val]), is_array(str, r, st), is_abstract(st[r -- _type] .type .class)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ oktype(val, ty, st) ↔ okval(val, ty)], [CSIMPSEQ : ⊦ fs ' ≠ _length ∧ fs ' ≠ _type → ( is_array (str, r, st[r0 -- fs ', val]) ↔ is_array(str, r, st))], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]])]]