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Proof step 74 from proof validrefs-putbyte-field (previous step)

refs1 = r1 + refs, r1 = (st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)][r0 -- mkfs(class0, ty0, fieldvar0) ']) .refval, 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, refs1, ty0, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), ∀ by, fieldvar, class, r, st, ty, str, refs0. # refs0 < # (r0 + refs1) → ( validrefs(str, refs0, ty, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]) → refs0 = [] ∨ junkref(str, refs0 .first, st) ∨ validrefs(str, refs0, ty, st)) ⊦ refs1 = [], r0 = jvmref, junkref(str, r0, st), validrefs(str, r0 ' + refs1, ty, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 73:
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)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ r + refs = r ' + refs])]]