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Proof step 18 from proof validrefs-putbyte-field (previous step)

st[r0 -- i '] = refval(r1), st[r0 -- _length] .intval ≤ i, 0 ≤ i, 0 < (st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)][r0 -- _length]) .intval, is_array(str, r0, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), st[r0 -- _type] .type ≤ ty, i < (st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)][r0 -- _length]) .intval, validrefs(str, r1 ' + refs, st[r0 -- _type] .type .type, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), is_array(str, r0, st), st[r0 -- _length] .intval < (st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)][r0 -- _length]) .intval, ∀ by, fieldvar, class, r, st0, ty, str, refs0. # refs0 < # (r0 + r1 + refs) → ( validrefs(str, refs0, ty, st0[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]) → refs0 = [] ∨ junkref(str, refs0 .first, st0) ∨ validrefs(str, refs0, ty, st0)) ⊦ r0 = jvmref, junkref(str, r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st[rk0, val][rk]) = st[rk] ,[rk, val, rk0, st] → [r0 -- _length, byteval(by), r -- mkfs(class, byte_type, fieldvar) ', st] ,F ,store ,javastore-ostorea ,At-other ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPFORWARD : ⊦ mkfs(class1, ty, fieldvar) ' = _length → class1 = `*Array*' .class ∧ ty = int_type ∧ fieldvar = `length' .field], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPSEQ : ⊦ int_type ≠ byte_type])], [EXTRATERMS : (r0 -- _length, byteval(by), r -- mkfs(class, byte_type, fieldvar) ', st)]]