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Proof step 14 from proof validrefs-delete-03 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
acc .first = st[r0 -- mkfs(class, ty0, fieldvar) '] .refval, 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, acc, ty0, st), ∀ str, ty, st, r. validrefs(str, acc, ty, st) → r ∈ acc ∨ validrefs(str, acc, ty, st -- r) ⊦ r = r0, r0 = jvmref, acc = [], r ∈ acc, ∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ']) ∧ acc .first = st[r0 -- fs '] .refval ∧ validrefs(str, acc, fs .type, st -- r)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ≠ r0 → (st -- r)[r0 -- sk0] = st[r0 -- sk0]], [CSIMPSEQ : ⊦ r ≠ r0 → ( is_obj(str, r0, st -- r) ↔ is_obj(str, r0, st))])]]