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Proof step 12 from proof ex-fits-validrefs-stronger (previous step)

sk .fs = mkfs(class0, ty, fieldvar), st[r -- _type] .type = mkclasstype(class), st[r -- sk] = refval(r0), is_obj(str, r, st), junkref(str, r0, st), fits(r0, sks0, st), sk ∈ instfields(class) ⊦ r = jvmref, validrefs(str, r ' + r0 ' + refs, mkclasstype(class), st) ∧ # refs = # sks0 ∧ (sks ⊑ sk ' + sks0 ∧ sks ≠ [] → st[r -- sks] .refval = (r ' + r0 ' + refs)[# sks]), mkfs(class0, ty, fieldvar) ' ∈ instfields(class) ∧ is_referencevalue(st[r -- mkfs(class0, ty, fieldvar) ']) ∧ st[r -- mkfs(class0, ty, fieldvar) '] .refval ≠ jvmref ∧ (¬ st[st[r -- mkfs(class0, ty, fieldvar) '] .refval -- _type] .type ≤ ty ∨ junkref(str, st[r -- mkfs(class0, ty, fieldvar) '] .refval, st))

User applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
sk .fs = mkfs(class0, ty, fieldvar), st[r -- _type] .type = mkclasstype(class), st[r -- sk] = refval(r0), is_obj(str, r, st), junkref(str, r0, st), fits(r0, sks0, st), sk ∈ instfields(class) ⊦ is_fskey(sk), r = jvmref, validrefs(str, r ' + r0 ' + refs, mkclasstype(class), st) ∧ # refs = # sks0 ∧ (sks ⊑ sk ' + sks0 ∧ sks ≠ [] → st[r -- sks] .refval = (r ' + r0 ' + refs)[# sks]), mkfs(class0, ty, fieldvar) ' ∈ instfields(class) ∧ is_referencevalue(st[r -- mkfs(class0, ty, fieldvar) ']) ∧ st[r -- mkfs(class0, ty, fieldvar) '] .refval ≠ jvmref ∧ (¬ st[st[r -- mkfs(class0, ty, fieldvar) '] .refval -- _type] .type ≤ ty ∨ junkref(str, st[r -- mkfs(class0, ty, fieldvar) '] .refval, st))

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_fskey(fs ')], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ ¬ junkref(str, jvmref, st)], [CSIMPELIM : ⊦ is_fskey(sk) → (fs = sk .fs ↔ sk = fs ')])], [EXTRATERMS : (sk, fs)]]