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Proof step 4 from proof validrefkeynotnull-put-statfield (previous step)

⊦ rk1 .ref = jvmref ∧ rk ≠ rk1 ∧ rk ∈ st ∧ validrefvalnotnull(str, st[rk], ty1, st) → validrefkeynotnull(str, rk, ty1, st[rk1, val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ validrefkeynotnull(str, rk, ty, st) ↔ rk ∈ st ∧ validrefvalnotnull(str, st[rk], ty, st)
Proof step 3:
⊦ rk1 .ref = jvmref ∧ rk ≠ rk1 ∧ validrefvalnotnull(str, val1, ty1, st) → validrefvalnotnull(str, val1, ty1, st[rk1, val])

Rule argument

[crewrite-arg: validrefkeynotnull-def , F , [st, ty, rk, str] → [st[rk1, val], ty1, rk, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st], [CSIMPSEQ : ⊦ rk ≠ rk0 → (st[rk0, val][rk]) = st[rk]])], [EXTRATERMS : (st[rk1, val], ty1, rk, str)]]