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Proof step 55 from proof validrefs-put-badclassfield-01 (previous step)

st[r0 -- _type] .type = mkclasstype(class), acc .first = st[r -- i '] .refval, is_array(str, r, st[r0 -- fs ', val]), is_arraytype(st[r -- _type] .type), is_array(str, r, st), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), validrefs(str, acc, st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval, ∀ st0, r1, str0, ty0, fs0, val0. is_classtype(st0[r1 -- _type] .type) ∧ validrefs(str0, acc, ty0, st0) → fs0 ' = _type ∨ junkref(str0, acc .first, st0) ∨ fs0 ' ∈ instfields(st0[r1 -- _type] .type .class) ∨ validrefs(str0, acc, ty0, st0[r1 -- fs0 ', val0]) ⊦ r = jvmref, fs ' = _type, acc = [], fs ' ∈ instfields(class), junkref(str, r, st), junkref(str, r, st[r0 -- fs ', val]), dups(acc .butlast), r ∈ acc .butlast, ¬ (st[r0 -- fs ', val][r -- _length]) .intval ≤ i ∧ validrefs(str, acc, st[r -- _type] .type .type, st[r0 -- fs ', val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 40:
⊦ rk ≠ rk0 → (st[rk0, val][rk]) = st[rk]
Proof step 54:
r -- _length ≠ r0 -- fs ', st[r0 -- _type] .type = mkclasstype(class), acc .first = st[r -- i '] .refval, is_array(str, r, st[r0 -- fs ', val]), is_arraytype(st[r -- _type] .type), is_array(str, r, st), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), validrefs(str, acc, st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval, ∀ st0, r1, str0, ty0, fs0, val0. is_classtype(st0[r1 -- _type] .type) ∧ validrefs(str0, acc, ty0, st0) → fs0 ' = _type ∨ junkref(str0, acc .first, st0) ∨ fs0 ' ∈ instfields(st0[r1 -- _type] .type .class) ∨ validrefs(str0, acc, ty0, st0[r1 -- fs0 ', val0]) ⊦ r = jvmref, fs ' = _type, acc = [], fs ' ∈ instfields(class), junkref(str, r, st), junkref(str, r, st[r0 -- fs ', val]), dups(acc .butlast), r ∈ acc .butlast, ¬ st[r -- _length] .intval ≤ i ∧ validrefs(str, acc, st[r -- _type] .type .type, st[r0 -- fs ', val])

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st[rk0, val][rk]) = st[rk] ,[rk, val, rk0, st] → [r -- _length, val, r0 -- fs ', st] ,F ,store ,javastore-ostorea ,At-other ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ is_array(str, r, st) → st[r -- _type] .type ≠ mkclasstype(class)])], [EXTRATERMS : (r -- _length, val, r0 -- fs ', st)]]