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

is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty, st[r -- mkfs(class, ty1, fieldvar) '] = refval(r0), junkrefs(str0, r0 ' + refs, ty1, st), level⊆(str, str0), st[r -- _type] .type ≤ ty, is_obj(str0, r, st), is_obj(str, r, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), ∀ str1, str2, ty0, st0. level⊆(str1, str2) ∧ junkrefs(str2, r0 ' + refs, ty0, st0) → junkrefs(str1, r0 ' + refs, ty0, st0) ⊦ r = jvmref, r0 ' + refs ≠ [] ∧ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ (r0 ' + refs) .first = st[r -- fs '] .refval ∧ junkrefs(str, r0 ' + refs, fs .type, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
st[r -- mkfs(class, ty1, fieldvar) '] = refval(r0), junkrefs(str0, r0 ' + refs, ty1, st), level⊆(str, str0), st[r -- _type] .type ≤ ty, is_obj(str0, r, st), is_obj(str, r, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), ∀ str1, str2, ty0, st0. level⊆(str1, str2) ∧ junkrefs(str2, r0 ' + refs, ty0, st0) → junkrefs(str1, r0 ' + refs, ty0, st0) ⊦ r = jvmref, ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ r0 = st[r -- fs '] .refval ∧ junkrefs(str, st[r -- fs '] .refval ' + refs, fs .type, st)

Rule argument

[emptyarg]

Additional information

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