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Proof step 12 from proof isobj-put-samefield-01 (previous step)

st[r -- _type] = typeval(mkclasstype(class)), okval(st[r -- mkfs(class0, ty, fieldvar) ', val][r -- sk], sk .fs .type), r -- sk ∈ st[r -- mkfs(class0, ty, fieldvar) ', val], is_fskey(sk), r -- _type ∈ st, r ∈ st, okval(val, ty), okval(st[r -- mkfs(class0, ty, fieldvar) '], ty), r -- mkfs(class0, ty, fieldvar) ' ∈ st, sk ∈ instfields(class), ¬ okval(st[r -- sk], sk .fs .type) ∨ ¬ r -- sk ∈ st, ∀ sk0. sk0 ∈ instfields(class) → is_fskey(sk0) ∧ r -- sk0 ∈ st[r -- mkfs(class0, ty, fieldvar) ', val] ∧ okval(st[r -- mkfs(class0, ty, fieldvar) ', val][r -- sk0], sk0 .fs .type) ⊦ r = jvmref, mkfs(class0, ty, fieldvar) ' = _type

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
sk = fs ', st[r -- _type] = typeval(mkclasstype(class)), okval(st[r -- mkfs(class0, ty, fieldvar) ', val][r -- sk], fs .type), r -- sk ∈ st[r -- mkfs(class0, ty, fieldvar) ', val], is_fskey(sk), r -- _type ∈ st, r ∈ st, okval(val, ty), okval(st[r -- mkfs(class0, ty, fieldvar) '], ty), r -- mkfs(class0, ty, fieldvar) ' ∈ st, sk ∈ instfields(class), ¬ okval(st[r -- sk], fs .type) ∨ ¬ r -- sk ∈ st, ∀ sk0. sk0 ∈ instfields(class) → is_fskey(sk0) ∧ r -- sk0 ∈ st[r -- mkfs(class0, ty, fieldvar) ', val] ∧ okval(st[r -- mkfs(class0, ty, fieldvar) ', val][r -- sk0], sk0 .fs .type) ⊦ r = jvmref, mkfs(class0, ty, fieldvar) ' = _type

Rule argument

[speclemmaarg: ,is_fskey(sk) → (fs = sk .fs ↔ sk = fs ') ,[sk, fs] → [sk, fs] ,T ,storekey , ,elim-03 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_fskey(sk) → (fs = sk .fs ↔ sk = fs ')])], [EXTRATERMS : (sk, fs)]]