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Proof step 15 from proof validrefs-subset-01 (previous step)

is_obj(str, r0, st), st[r0 -- mkfs(class, ty1, fieldvar) '] = refval(r), r0 ∈ st, st[r0 -- _type] .type ≤ ty, is_obj(str, r0, st), st ⊆ st0, mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), validrefs(str, r ' + refs, ty1, st), r0 -- _type ∈ st, r0 -- mkfs(class, ty1, fieldvar) ' ∈ st, ∀ str0, ty0, st1, st2. validrefs(str0, r ' + refs, ty0, st1) ∧ st1 ⊆ st2 ∧ ¬ junkref(str0, r, st1) → validrefs(str0, r ' + refs, ty0, st2) ⊦ r0 = jvmref, mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- mkfs(class, ty1, fieldvar) ']) ∧ st[r0 -- mkfs(class, ty1, fieldvar) '] .refval ≠ jvmref ∧ ( ¬ st[st[r0 -- mkfs(class, ty1, fieldvar) '] .refval -- _type] .type ≤ mkfs(class, ty1, fieldvar) .type ∨ junkref(str, st[r0 -- mkfs(class, ty1, fieldvar) '] .refval, st)), validrefs(str, r ' + refs, ty1, st0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
⊦ validrefs(str, jvmref ' + refs, ty, st) ↔ refs = []
Proof step 14:
st[r0 -- mkfs(class, ty1, fieldvar) '] = refval(r), r0 -- mkfs(class, ty1, fieldvar) ' ∈ st, r0 -- _type ∈ st, validrefs(str, r ' + refs, ty1, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), st ⊆ st0, is_obj(str, r0, st), st[r0 -- _type] .type ≤ ty, r0 ∈ st, st[r -- _type] .type ≤ ty1, ∀ str0, ty0, st1, st2. validrefs(str0, r ' + refs, ty0, st1) ∧ st1 ⊆ st2 ∧ ¬ junkref(str0, r, st1) → validrefs(str0, r ' + refs, ty0, st2) ⊦ r0 = jvmref, r = jvmref, validrefs(str, r ' + refs, ty1, st0), junkref(str, r, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) .type = ty], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]