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Proof step 144 from proof validref-refs-last-valid-subset (previous step)

acc + r1 ' = r2 + refs ∧ acc + r1 ' ≠ [], r2 = st0[r0 -- mkfs(class, ty0, fieldvar) '] .refval, is_obj(str, r0, st0), validref(str, r, st[r -- _type] .type, st), st ⊆ st0, st0[r0 -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st0[r0 -- _type] .type .class), is_referencevalue(st0[r0 -- mkfs(class, ty0, fieldvar) ']), validrefs(str, acc + r1 ', ty0, st0), ∀ str, r, st, st0, r1, ty. validref(str, r, st[r -- _type] .type, st) ∧ st ⊆ st0 ∧ r ∈ acc ∧ validrefs(str, acc + r1 ', ty, st0) → validref(str, r1, st[r1 -- _type] .type, st) ⊦ r0 = jvmref, validref(str, r1, st[r1 -- _type] .type, st), r ≠ r0 ∧ ¬ r ∈ acc

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 143:
acc + r1 ' = st0[r0 -- mkfs(class, ty0, fieldvar) '] .refval ' + refs, validrefs(str, acc + r1 ', ty0, st0), is_referencevalue(st0[r0 -- mkfs(class, ty0, fieldvar) ']), mkfs(class, ty0, fieldvar) ' ∈ instfields(st0[r0 -- _type] .type .class), st0[r0 -- _type] .type ≤ ty, st ⊆ st0, validref(str, r, st[r -- _type] .type, st), is_obj(str, r0, st0), ∀ str, r, st, st0, r1, ty. validref(str, r, st[r -- _type] .type, st) ∧ st ⊆ st0 ∧ r ∈ acc ∧ validrefs(str, acc + r1 ', ty, st0) → validref(str, r1, st[r1 -- _type] .type, st) ⊦ r0 = jvmref, validref(str, r1, st[r1 -- _type] .type, st), r ≠ r0 ∧ ¬ r ∈ acc, r1 ≠ st0[r0 -- mkfs(class, ty0, fieldvar) '] .refval ∧ ¬ r1 ∈ refs, ¬ st0[r0 -- mkfs(class, ty0, fieldvar) '] .refval ∈ acc ∧ st0[r0 -- mkfs(class, ty0, fieldvar) '] .refval ≠ r1

Rule argument

[emptyarg]

Additional information

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