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Proof step 13 from proof validrefs-junkrefs-append (previous step)

is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty, st[r -- _type] .type ≤ ty, is_obj(str, r, st), r0 ' + refs2 = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ (r0 ' + refs2) .first = st[r -- fs '] .refval ∧ validrefs(str, r0 ' + refs2, fs .type, st)), junkrefs(str, (r0 ' + refs2) .last ' + refs1, st[(r0 ' + refs2) .last -- _type] .type, st), ∀ str0, ty0, st0, refs. validrefs(str0, r0 ' + refs2, ty0, st0) ∧ junkrefs(str0, (r0 ' + refs2) .last ' + refs, st0[(r0 ' + refs2) .last -- _type] .type, st0) → junkrefs(str0, (r0 ' + refs2) + refs, ty0, st0) ⊦ r = jvmref, ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ r0 = st[r -- fs '] .refval ∧ junkrefs(str, (st[r -- fs '] .refval ' + refs2) + refs1, fs .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
validrefs(str, st[r -- fs '] .refval ' + refs2, fs .type, st), is_referencevalue(st[r -- fs ']), fs ' ∈ instfields(st[r -- _type] .type .class), junkrefs(str, (st[r -- fs '] .refval ' + refs2) .last ' + refs1, st[(st[r -- fs '] .refval ' + refs2) .last -- _type] .type, st), is_obj(str, r, st), st[r -- _type] .type ≤ ty, ∀ str0, ty0, st0, refs. validrefs(str0, st[r -- fs '] .refval ' + refs2, ty0, st0) ∧ junkrefs(str0, (st[r -- fs '] .refval ' + refs2) .last ' + refs, st0[(st[r -- fs '] .refval ' + refs2) .last -- _type] .type, st0) → junkrefs(str0, (st[r -- fs '] .refval ' + refs2) + refs, ty0, st0) ⊦ r = jvmref, ∃ fs0. fs0 ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs0 ']) ∧ st[r -- fs '] .refval = st[r -- fs0 '] .refval ∧ junkrefs(str, (st[r -- fs0 '] .refval ' + refs2) + refs1, fs0 .type, st)

Rule argument

[emptyarg]

Additional information

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