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Proof step 48 from proof compat-put (previous step)

sk .fs = mkfs(class1, ty0, fieldvar0), compat(str, st[jvmref -- sk], ty0, st), sk ∈ statfields(class0), compatmode(str, st), compatrefs(str, st), compat(str, val, ty, st), initdone(class0, st), compatfields(str, jvmref, statfields(class0), st), class∃(str, class0) ∨ interface∃(str, class0), jvmref ≠ r ∨ sk ≠ mkfs(class, ty, fieldvar) ' ⊦ mkfs(class, ty, fieldvar) ' = _length, r -- mkfs(class, ty, fieldvar) ' = _uninit, ty = void_type, jvmref = r ∧ sk = mkfs(class, ty, fieldvar) ', jvmref -- sk ∈ st ∧ ¬ is_indexkey(sk)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 46:
⊦ compatfields(str, r, sks, st) ↔ (∀ sk. sk ∈ sks → r -- sk ∈ st ∧ is_fskey(sk) ∧ compat(str, st[r -- sk], sk .fs .type, st))
Proof step 47:
sk .fs = mkfs(class1, ty0, fieldvar0), compat(str, st[jvmref -- sk], ty0, st), sk ∈ statfields(class0), compatmode(str, st), compatrefs(str, st), compat(str, val, ty, st), initdone(class0, st), ∀ sk. sk ∈ statfields(class0) → jvmref -- sk ∈ st ∧ is_fskey(sk) ∧ compat(str, st[jvmref -- sk], sk .fs .type, st), class∃(str, class0) ∨ interface∃(str, class0), jvmref ≠ r ∨ sk ≠ mkfs(class, ty, fieldvar) ' ⊦ mkfs(class, ty, fieldvar) ' = _length, r -- mkfs(class, ty, fieldvar) ' = _uninit, ty = void_type, jvmref = r ∧ sk = mkfs(class, ty, fieldvar) ', jvmref -- sk ∈ st ∧ ¬ is_indexkey(sk)

Rule argument

[crewrite-arg: fields-compat , F , [st, sks, r, str] → [st, statfields(class0), jvmref, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, statfields(class0), jvmref, str)]]