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Proof step 62 from proof validrefs-putbyte-field (previous step)

¬ (r0 ≠ jvmref ∧ ¬ is_valid_ref(str, r0, st)), st[r0 -- mkfs(class0, ty0, fieldvar0) '] = refval(r1), is_obj(str, r0, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), st[r0 -- _type] .type ≤ ty, mkfs(class0, ty0, fieldvar0) ' ∈ instfields(st[r0 -- _type] .type .class), validrefs(str, r1 ' + refs, ty0, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), is_obj(str, r0, st), junkref(str, r1, st), ∀ by0, fieldvar1, class1, r2, st0, ty, str, refs0. # refs0 < # (r0 + r1 + refs) → ( validrefs(str, refs0, ty, st0[r2 -- mkfs(class1, byte_type, fieldvar1) ', byteval(by0)]) → refs0 = [] ∨ junkref(str, refs0 .first, st0) ∨ validrefs(str, refs0, ty, st0)) ⊦ r0 = jvmref, ty0 = byte_type, junkref(str, r0, st), validrefs(str, r1 ' + refs, ty0, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 61:
st[r0 -- mkfs(class0, ty0, fieldvar0) '] = refval(r1), is_obj(str, r0, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), st[r0 -- _type] .type ≤ ty, mkfs(class0, ty0, fieldvar0) ' ∈ instfields(st[r0 -- _type] .type .class), validrefs(str, r1 ' + refs, ty0, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), is_obj(str, r0, st), junkref(str, r1, st), ∀ by0, fieldvar1, class1, r2, st0, ty, str, refs0. # refs0 < # (r0 + r1 + refs) → ( validrefs(str, refs0, ty, st0[r2 -- mkfs(class1, byte_type, fieldvar1) ', byteval(by0)]) → refs0 = [] ∨ junkref(str, refs0 .first, st0) ∨ validrefs(str, refs0, ty, st0)) ⊦ r0 = jvmref, ty0 = byte_type, junkref(str, r0, st), validrefs(str, r1 ' + refs, ty0, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_obj(str, r, st) → is_valid_ref(str, r, st)], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]