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Proof step 23 from proof validrefs-delcycle-01 (previous step)

is_obj(str, r0, st) ∧ st[r0 -- _type] .type ≤ ty, is_obj(str, r0, st), acc + r ' + refs0 + r ' + refs1 = [] ∨ (∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ']) ∧ (acc + r ' + refs0 + r ' + refs1) .first = st[r0 -- fs '] .refval ∧ validrefs(str, acc + r ' + refs0 + r ' + refs1, fs .type, st)), st[r0 -- _type] .type ≤ ty, ∀ str, r, refs0, refs1, ty, st. validrefs(str, acc + r ' + refs0 + r ' + refs1, ty, st) → validrefs(str, acc + r ' + refs1, ty, st) ⊦ r0 = jvmref, validrefs(str, (r0 ' + acc) + r ' + refs1, ty, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
(acc + r ') .first = st[r0 -- fs '] .refval, is_obj(str, r0, st), st[r0 -- _type] .type ≤ ty, fs ' ∈ instfields(st[r0 -- _type] .type .class), is_referencevalue(st[r0 -- fs ']), validrefs(str, acc + r ' + refs0 + r ' + refs1, fs .type, st), ∀ str, r, refs0, refs1, ty, st. validrefs(str, acc + r ' + refs0 + r ' + refs1, ty, st) → validrefs(str, acc + r ' + refs1, ty, st) ⊦ r0 = jvmref, validrefs(str, (r0 ' + acc) + r ' + refs1, ty, st)

Rule argument

[emptyarg]

Additional information

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