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Proof step 15 from proof is_valid_ref-put-equiv (previous step)

⊦ okval(st[r1 -- sk], sk .fs .type) ∧ r1 -- sk ∈ st ∧ is_fskey(sk) ∧ okval(val, sk .fs .type) ∧ sk .fs .type ≠ void_type ∧ sk ≠ _length → (is_obj(str, r, st[r1 -- sk, val]) ∨ is_array(str, r, st[r1 -- sk, val]) ↔ is_valid_ref(str, r, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ okval(st[r1 -- sk], sk .fs .type) ∧ r1 -- sk ∈ st ∧ is_fskey(sk) ∧ okval(val, sk .fs .type) ∧ sk .fs .type ≠ void_type → (is_obj(str, r, st[r1 -- sk, val]) ↔ is_obj(str, 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:
⊦ is_valid_ref(str, r, st) ↔ is_obj(str, r, st) ∨ is_array(str, r, st)
Proof step 14:
okval(st[r1 -- sk], sk .fs .type) ∧ r1 -- sk ∈ st ∧ is_fskey(sk) ∧ okval(val, sk .fs .type) ∧ sk .fs .type ≠ void_type ⊦ okval(st[r1 -- sk], sk .fs .type) ∧ r1 -- sk ∈ st ∧ is_fskey(sk) ∧ okval(val, sk .fs .type) ∧ sk .fs .type ≠ void_type ∧ sk ≠ _length → (is_obj(str, r, st) ∨ is_array(str, r, st[r1 -- sk, val]) ↔ is_valid_ref(str, r, st))

Rule argument

[crewrite-arg: is_obj-put-equiv , F , [val, sk, r1, st, r, str] → [val, sk, r1, st, r, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)], [CSIMPSEQ : ⊦ is_indexkey(sk) → ¬ is_fskey(sk)])], [EXTRATERMS : (val, sk, r1, st, r, str)]]