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Proof step 20 from proof validrefs-append (previous step)

st[r0 -- mkfs(class, ty1, fieldvar) '] = refval(r1), acc + r ' = r1 ' + refs, validrefs(str, acc + r ', ty1, st), is_referencevalue(st[r0 -- mkfs(class, ty1, fieldvar) ']), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), st[r0 -- _type] .type ≤ ty, validrefs(str, r ' + refs0, ty0, st), is_obj(str, r0, st), ∀ str, r, refs0, ty0, st, ty. validrefs(str, r ' + refs0, ty0, st) ∧ validrefs(str, acc + r ', ty, st) → validrefs(str, acc + r ' + refs0, ty, st) ⊦ r0 = jvmref, validrefs(str, (r0 ' + acc) + r ' + refs0, ty, st), r ≠ r1 ∧ ¬ r ∈ refs, ¬ r1 ∈ acc ∧ r1 ≠ r

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
acc + r ' = r1 ' + refs, st[r0 -- mkfs(class, ty1, fieldvar) '] = refval(r1), is_obj(str, r0, st), validrefs(str, r ' + refs0, ty0, st), st[r0 -- _type] .type ≤ ty, mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), validrefs(str, r1 ' + refs, ty1, st), ∀ str, r, refs0, ty0, st, ty. validrefs(str, r ' + refs0, ty0, st) ∧ validrefs(str, acc + r ', ty, st) → validrefs(str, acc + r ' + refs0, ty, st) ⊦ r0 = jvmref, validrefs(str, (r0 ' + acc) + r ' + refs0, ty, st), r ≠ r1 ∧ ¬ r ∈ refs, ¬ r1 ∈ acc ∧ r1 ≠ r

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPSEQ : ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)], [CSIMPFORWARD : ⊦ r ' + refs = refs0 → r ∈ refs0], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPFORWARD : ⊦ refs + r ' = refs0 → r ∈ refs0])]]