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Proof step 10 from proof validrefs-not-in-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
⊦ ¬ is_valid_ref(str, r, st) → (validrefs(str, r ' + refs, ty, st) ↔ r = jvmref ∧ refs = [])
Proof step 9:
is_obj(str, r0, st), st[r0 -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), is_referencevalue(st[r0 -- mkfs(class, ty0, fieldvar) ']), validrefs(str, st[r0 -- mkfs(class, ty0, fieldvar) '] .refval ' + refs, ty0, st), r ∈ refs, ∀ r1, str0, ty1, st0. (r1 = st[r0 -- mkfs(class, ty0, fieldvar) '] .refval ∨ r1 ∈ refs) ∧ validrefs(str0, st[r0 -- mkfs(class, ty0, fieldvar) '] .refval ' + refs, ty1, st0) → r1 = jvmref ∨ is_valid_ref(str0, r1, st0) ⊦ r0 = jvmref, r = r0, r = jvmref, r = st[r0 -- mkfs(class, ty0, fieldvar) '] .refval, is_valid_ref(str, r, st)

Rule argument

[emptyarg]

Additional information

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