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Proof step 9 from proof validrefs-junkrefs-01 (previous step)

acc = [], st[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), acc + refs0 = r0 ' + refs, is_obj(str, r, st), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), junkrefs(str, acc + refs0, ty0, st), st[r -- _type] .type ≤ ty, ∀ str, refs0, ty, st. junkrefs(str, acc + refs0, ty, st) → junkrefs(str, acc, ty, st) ∨ validrefs(str, acc, ty, st) ⊦ r = jvmref, acc + refs0 = [], validrefs(str, r ' + acc, ty, st), ¬ r0 ∈ acc ∧ ¬ r0 ∈ refs0, acc ≠ [] ∧ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ acc .first = st[r -- fs '] .refval ∧ junkrefs(str, acc, fs .type, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
⊦ validrefs(str, [], ty, st)
Proof step 8:
st[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), junkrefs(str, r0 ' + refs, ty0, st), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), st[r -- _type] .type ≤ ty ⊦ r = jvmref, validrefs(str, r ', ty, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPSEQ : ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPFORWARD : ⊦ r ' + refs = refs0 → r ∈ refs0], [CSIMPSEQ : ⊦ ¬ r ∈ []], [CSIMPSEQ : ⊦ ¬ junkrefs(str, [], ty, st)], [CSIMPSEQ : ⊦ refs + [] = refs], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ [] + refs = refs])]]