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Proof step 12 from proof validrefs-addarray (previous step)

acc = r1 + refs, r1 = st[r0 -- mkfs(class, ty1, fieldvar) '] .refval, newref(r, st), st[r0 -- _type] .type ≤ ty, is_obj(str, r0, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), is_referencevalue(st[r0 -- mkfs(class, ty1, fieldvar) ']), validrefs(str, acc, ty1, addarray(r, ty0, vals, st)), ∀ str, ty, r, ty0, vals, st. validrefs(str, acc, ty, addarray(r, ty0, vals, st)) ∧ newref(r, st) → r = jvmref ∨ r ∈ acc ∨ validrefs(str, acc, ty, st) ⊦ r = jvmref, r = r0, r0 = jvmref, acc = [], r ∈ acc, ∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ']) ∧ r1 = st[r0 -- fs '] .refval ∧ validrefs(str, acc, fs .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
newref(r, st), st[r0 -- _type] .type ≤ ty, is_obj(str, r0, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), is_referencevalue(st[r0 -- mkfs(class, ty1, fieldvar) ']), validrefs(str, st[r0 -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, ty1, addarray(r, ty0, vals, st)), ∀ str0, ty2, r1, ty3, vals0, st0. validrefs(str0, st[r0 -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, ty2, addarray(r1, ty3, vals0, st0)) ∧ newref(r1, st0) → r1 = jvmref ∨ r1 = st[r0 -- mkfs(class, ty1, fieldvar) '] .refval ∨ r1 ∈ refs ∨ validrefs(str0, st[r0 -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, ty2, st0) ⊦ r = jvmref, r = r0, r0 = jvmref, r = st[r0 -- mkfs(class, ty1, fieldvar) '] .refval, r ∈ refs, ∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ']) ∧ st[r0 -- mkfs(class, ty1, fieldvar) '] .refval = st[r0 -- fs '] .refval ∧ validrefs(str, st[r0 -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, fs .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPSEQ : ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)], [CSIMPSEQ : ⊦ ¬ r ∈ r0 ' + refs ↔ r ≠ r0 ∧ ¬ r ∈ refs], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ r + refs = r ' + refs])]]