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Proof step 100 from proof compat-put (previous step)

st[r0 -- _type] = typeval(mkclasstype(class0)), compat(str, val, ty, st), compatstatic(str, st), compatmode(str, st), r0 -- _type ∈ st[r -- mkfs(class, ty, fieldvar) ', val], r0 ∈ st[r -- mkfs(class, ty, fieldvar) ', val], r0 -- _type ∈ st, r0 ∈ st, compatfields(str, r0, instfields(class0), st), class+∃(str, class0) ⊦ r0 = jvmref, ty = void_type, mkfs(class, ty, fieldvar) ' = _length, compatfields(str, r0, instfields(class0), st[r -- mkfs(class, ty, fieldvar) ', val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 74:
⊦ 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 99:
st[r0 -- _type] = typeval(mkclasstype(class0)), compat(str, val, ty, st), compatstatic(str, st), compatmode(str, st), r0 -- _type ∈ st[r -- mkfs(class, ty, fieldvar) ', val], r0 ∈ st[r -- mkfs(class, ty, fieldvar) ', val], r0 -- _type ∈ st, r0 ∈ st, compatfields(str, r0, instfields(class0), st), class+∃(str, class0) ⊦ r0 = jvmref, ty = void_type, mkfs(class, ty, fieldvar) ' = _length, ∀ sk. sk ∈ instfields(class0) → r0 -- sk ∈ st[r -- mkfs(class, ty, fieldvar) ', val] ∧ is_fskey(sk) ∧ compat(str, st[r -- mkfs(class, ty, fieldvar) ', val][r0 -- sk], sk .fs .type, st[r -- mkfs(class, ty, fieldvar) ', val])

Rule argument

[crewrite-arg: fields-compat , F , [st, sks, r, str] → [st[r -- mkfs(class, ty, fieldvar) ', val], instfields(class0), r0, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r -- mkfs(class, ty, fieldvar) ', val], instfields(class0), r0, str)]]