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Proof step 73 from proof validrefs-putbyte-field (previous step)

is_obj(str, r0, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), st[r0 -- _type] .type ≤ ty, mkfs(class0, ty0, fieldvar0) ' ∈ instfields(st[r0 -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)][r0 -- mkfs(class0, ty0, fieldvar0) ']), validrefs (str, (st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)][r0 -- mkfs(class0, ty0, fieldvar0) ']) .refval ' + refs, ty0, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), ∀ by0, fieldvar1, class1, r2, st0, ty, str, refs0. # refs0 < # (r0 + (st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)][r0 -- mkfs(class0, ty0, fieldvar0) ']) .refval + 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)) ⊦ r0 = jvmref, junkref(str, r0, st), validrefs(str, r0 ' + (st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)][r0 -- mkfs(class0, ty0, fieldvar0) ']) .refval ' + refs, ty, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 72:
(st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)][r0 -- mkfs(class0, ty0, fieldvar0) ']) = refval(r1), is_obj(str, r0, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), st[r0 -- _type] .type ≤ ty, mkfs(class0, ty0, fieldvar0) ' ∈ instfields(st[r0 -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)][r0 -- mkfs(class0, ty0, fieldvar0) ']), validrefs(str, r1 ' + refs, ty0, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), ∀ by0, fieldvar1, class1, r2, st0, ty, str, refs0. # refs0 < # (r0 + 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)) ⊦ r0 = jvmref, junkref(str, r0, st), validrefs(str, r0 ' + r1 ' + refs, ty, st)

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)] [r0 -- mkfs(class0, ty0, fieldvar0) ' ], r1] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)] [r0 -- mkfs(class0, ty0, fieldvar0) ' ], r1)]]