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Proof step 13 from proof validrefs-putbyte-field (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 12:
st[r0 -- i '] = refval(r1), validrefs(str, r1 ' + refs, st[r0 -- _type] .type .type, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), i < (st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)][r0 -- _length]) .intval, st[r0 -- _type] .type ≤ ty, is_array(str, r0, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), 0 < (st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)][r0 -- _length]) .intval, 0 ≤ i, is_obj(str, r0, st), ∀ 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 -- _length = r -- mkfs(class, byte_type, fieldvar) ', r0 = jvmref, validrefs(str, r0 ' + r1 ' + refs, ty, st), junkref(str, r0, st)

Rule argument

[fma-arg: r0 -- _length = r -- mkfs(class, byte_type, fieldvar) ']

Additional information

[[CONCRETESIMPRULES : ([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 ∧ j < j0 → i < j0], [CSIMPSEQ : ⊦ int_type ≠ byte_type])], [EXTRAFMAS : (r0 -- _length = r -- mkfs(class, byte_type, fieldvar) ')]]