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

acc = r0 + refs, r0 = st[r -- mkfs(class, ty, fieldvar) '] .refval, is_obj(str0, r, st), st[r -- _type] .type ≤ ty0, level⊆(str, str0), is_obj(str, r, st), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty, fieldvar) ']), validrefs(str, acc, ty, st), ∀ str, ty0, st, str0. validrefs(str, acc, ty0, st) ∧ level⊆(str, str0) → validrefs(str0, acc, ty0, st) ⊦ r = jvmref, acc = [], ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ r0 = st[r -- fs '] .refval ∧ validrefs(str0, acc, fs .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
is_obj(str0, r, st), st[r -- _type] .type ≤ ty0, level⊆(str, str0), is_obj(str, r, st), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty, fieldvar) ']), validrefs(str, st[r -- mkfs(class, ty, fieldvar) '] .refval ' + refs, ty, st), ∀ str1, ty1, st0, str2. validrefs(str1, st[r -- mkfs(class, ty, fieldvar) '] .refval ' + refs, ty1, st0) ∧ level⊆(str1, str2) → validrefs(str2, st[r -- mkfs(class, ty, fieldvar) '] .refval ' + refs, ty1, st0) ⊦ r = jvmref, ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ st[r -- mkfs(class, ty, fieldvar) '] .refval = st[r -- fs '] .refval ∧ validrefs(str0, st[r -- mkfs(class, ty, fieldvar) '] .refval ' + refs, fs .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ r + refs = r ' + refs])]]