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Proof step 38 from proof validrefs-put-badclassfield (previous step)

st[r0 -- _type] .type = mkclasstype(class), validrefs(str, (st[r0 -- fs ', val][r -- fs0 ']) .refval ' + refs, fs0 .type, st[r0 -- fs ', val]), is_referencevalue(st[r0 -- fs ', val][r -- fs0 ']), fs0 ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st[r0 -- fs ', val]), st[r -- _type] .type ≤ ty, is_obj(str, r, st), ∀ str0, ty0, st0, fs1, r2, val0. ¬ validrefs(str0, (st[r0 -- fs ', val][r -- fs0 ']) .refval ' + refs, ty0, st0) ∧ ¬ junkref(str0, (st[r0 -- fs ', val][r -- fs0 ']) .refval, st0) ∧ fs1 ' ≠ _type ∧ is_classtype(st0[r2 -- _type] .type) ∧ ¬ fs1 ' ∈ instfields(st0[r2 -- _type] .type .class) → ¬ validrefs(str0, (st[r0 -- fs ', val][r -- fs0 ']) .refval ' + refs, ty0, st0[r2 -- fs1 ', val0]) ⊦ fs ' = _type, r = jvmref, dups(((st[r0 -- fs ', val][r -- fs0 ']) .refval ' + refs) .butlast), r ∈ ((st[r0 -- fs ', val][r -- fs0 ']) .refval ' + refs) .butlast, fs ' ∈ instfields(class), junkref(str, r, st), validrefs(str, r ' + (st[r0 -- fs ', val][r -- fs0 ']) .refval ' + refs, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ rk ≠ rk0 → (st[rk0, val][rk]) = st[rk]
Proof step 37:
r -- fs0 ' ≠ r0 -- fs ', st[r0 -- _type] .type = mkclasstype(class), validrefs(str, st[r -- fs0 '] .refval ' + refs, fs0 .type, st[r0 -- fs ', val]), is_referencevalue(st[r -- fs0 ']), fs0 ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st[r0 -- fs ', val]), st[r -- _type] .type ≤ ty, is_obj(str, r, st), ∀ str0, ty0, st0, fs1, r2, val0. ¬ validrefs(str0, st[r -- fs0 '] .refval ' + refs, ty0, st0) ∧ ¬ junkref(str0, st[r -- fs0 '] .refval, st0) ∧ fs1 ' ≠ _type ∧ is_classtype(st0[r2 -- _type] .type) ∧ ¬ fs1 ' ∈ instfields(st0[r2 -- _type] .type .class) → ¬ validrefs(str0, st[r -- fs0 '] .refval ' + refs, ty0, st0[r2 -- fs1 ', val0]) ⊦ fs ' = _type, r = jvmref, dups((st[r -- fs0 '] .refval ' + refs) .butlast), r ∈ (st[r -- fs0 '] .refval ' + refs) .butlast, fs ' ∈ instfields(class), junkref(str, r, st), validrefs(str, r ' + st[r -- fs0 '] .refval ' + refs, ty, st)

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st[rk0, val][rk]) = st[rk] ,[rk, val, rk0, st] → [r -- fs0 ', val, r0 -- fs ', st] ,F ,store ,javastore-ostorea ,At-other ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ fs ' = fs0 ' ↔ fs = fs0], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ (st[rk, val][rk]) = val], [CSIMPSEQ : ⊦ mkclasstype(class) .class = class], [CSIMPSEQ : ⊦ mkclasstype(class) ≤ ty ↔ is_classtype(ty) ∧ class ≤ ty .class])], [EXTRATERMS : (r -- fs0 ', val, r0 -- fs ', st)]]