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Proof step 25 from proof compatfields-mode (previous step)

⊦ r = jvmref, (∀ sk. sk ∈ instfields(class) → r -- sk ∈ st ∧ is_fskey(sk) ∧ compat(str, st[r -- sk], sk .fs .type, st[_mode, val])) ↔ (∀ sk. sk ∈ instfields(class) → r -- sk ∈ st ∧ ¬ is_indexkey(sk) ∧ compat(str, st[r -- sk], sk .fs .type, st))

User applied rule case distinction

And obtained the following new goals

Proof step 13:
∀ sk. sk ∈ instfields(class) → r -- sk ∈ st ∧ is_fskey(sk) ∧ compat(str, st[r -- sk], sk .fs .type, st[_mode, val]) ⊦ ∀ sk. sk ∈ instfields(class) → r -- sk ∈ st ∧ ¬ is_indexkey(sk) ∧ compat(str, st[r -- sk], sk .fs .type, st), r = jvmref
Proof step 24:
∀ sk. sk ∈ instfields(class) → r -- sk ∈ st ∧ ¬ is_indexkey(sk) ∧ compat(str, st[r -- sk], sk .fs .type, st) ⊦ ∀ sk. sk ∈ instfields(class) → r -- sk ∈ st ∧ is_fskey(sk) ∧ compat(str, st[r -- sk], sk .fs .type, st[_mode, val]), r = jvmref

Rule argument

[CASEDARG : pos: right 2, ()]

Additional information

[[CONCRETESIMPRULES : ()]]