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Proof step 51 from proof validrefs-putbyte-field (previous step)

st[r -- mkfs(class0, ty0, fieldvar0) '] = refval(r1), is_array(str, r, st), is_obj(str, r, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), st[r -- _type] .type ≤ ty, mkfs(class0, ty0, fieldvar0) ' ∈ instfields(st[r -- _type] .type .class), validrefs(str, r1 ' + refs, ty0, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), fieldvar0 ≠ fieldvar ∨ ty0 ≠ byte_type ∨ class0 ≠ class, ∀ by0, fieldvar1, class1, r2, st0, ty, str, refs0. # refs0 < # (r + r1 + refs) → ( validrefs(str, refs0, ty, st0[r2 -- mkfs(class1, byte_type, fieldvar1) ', byteval(by0)]) → refs0 = [] ∨ junkref(str, refs0 .first, st0) ∨ validrefs(str, refs0, ty, st0)) ⊦ r = jvmref, junkref(str, r, st), validrefs(str, r ' + r1 ' + refs, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: ,¬ is_classtype(st[r -- _type] .type) → ¬ is_obj(str, r, st) ,[st, r, str] → [st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)], r, str] ,F ,addfuns , ,is_obj-classtype ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (st[ r0 -- mkfs (class, byte_type, fieldvar) ', val] [r -- _type ] ) = st[r -- _type]], [CSIMPSEQ : ⊦ is_classtype (st[r -- _type] .type) → ¬ is_array(str, r, st)])], [EXTRATERMS : (st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)], r, str)]]