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Proof step 65 from proof validrefs-putbyte-field (previous step)

st[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), validrefs(str, r1 ' + refs, ty0, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), is_obj(str, r0, st), ∀ 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, ty0 = byte_type, junkref(str, r0, st), validrefs(str, r1 ' + refs, ty0, st)

User applied rule apply induction

And obtained the following new goals

Proof step 64:
r1 ' + refs = [] ∨ junkref(str, (r1 ' + refs) .first, st) ∨ validrefs(str, r1 ' + refs, ty0, st), st[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), validrefs(str, r1 ' + refs, ty0, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), is_obj(str, r0, st), ∀ 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, ty0 = byte_type, junkref(str, r0, st), validrefs(str, r1 ' + refs, ty0, st)

Rule argument

[substlist-arg: [by0, fieldvar1, class1, r2, st0, ty, str, refs0] → [by, fieldvar, class, r, st, ty0, str, r1 ' + refs] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ # (refs + refs0) = # refs + # refs0], [CSIMPSEQ : ⊦ # r ' = 0 +1], [CSIMPSEQ : ⊦ r + refs = r ' + refs], [CSIMPSEQ : ⊦ m + n < m + n0 ↔ n < n0], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (by, fieldvar, class, r, st, ty0, str, r1 ' + refs)]]