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Proof step 19 from proof validrefs-addarray-junkref (previous step)

is_obj(str, r1, addarray(r, ty, vals, st)) ∧ (addarray(r, ty, vals, st)[r1 -- _type]) .type ≤ ty0, is_obj(str, r1, addarray(r, ty, vals, st)), r2 ' + refs = [] ∨ (∃ fs. fs ' ∈ instfields((addarray(r, ty, vals, st)[r1 -- _type]) .type .class) ∧ is_referencevalue(addarray(r, ty, vals, st)[r1 -- fs ']) ∧ (r2 ' + refs) .first = (addarray(r, ty, vals, st)[r1 -- fs ']) .refval ∧ validrefs(str, r2 ' + refs, fs .type, addarray(r, ty, vals, st))), newref(r, st), st[r1 -- _type] .type ≤ ty0, ∀ str0, ty1, r0, ty2, vals0, st0. validrefs(str0, r2 ' + refs, ty1, addarray(r0, ty2, vals0, st0)) ∧ newref(r0, st0) ∧ (r0 = r2 ∨ r0 ∈ refs) → junkref(str0, r2, st0) ⊦ r1 = jvmref, r = jvmref, r = r1, junkref(str, r1, st), r ≠ r2 ∧ ¬ r ∈ refs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
validrefs(str, st[r1 -- fs '] .refval ' + refs, fs .type, addarray(r, ty, vals, st)), is_referencevalue(st[r1 -- fs ']), fs ' ∈ instfields(st[r1 -- _type] .type .class), is_obj(str, r1, st), st[r1 -- _type] .type ≤ ty0, newref(r, st), ∀ str0, ty1, r0, ty2, vals0, st0. validrefs(str0, st[r1 -- fs '] .refval ' + refs, ty1, addarray(r0, ty2, vals0, st0)) ∧ newref(r0, st0) ∧ (r0 = st[r1 -- fs '] .refval ∨ r0 ∈ refs) → junkref(str0, st[r1 -- fs '] .refval, st0) ⊦ r = r1, r = jvmref, r1 = jvmref, junkref(str, r1, st), r ≠ st[r1 -- fs '] .refval ∧ ¬ r ∈ refs

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 = []], [CSIMPSEQ : ⊦ r ≠ r0 → ( is_obj (str, r, addarray(r0, ty0, vals, st)) ↔ is_obj(str, r, st))], [CSIMPSEQ : ⊦ r ≠ r0 → (addarray(r, ty, vals, st) [r0 -- sk ] ) = st[r0 -- sk]])]]