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Proof step 16 from proof validsubset-trans (previous step)

r0 ∈ st1, junkref(str, r0, st1), ∀ r, ty. validref(str, r, ty, st) → validref(str, r, ty, st0), ∀ r. ¬ r ∈ st0 ∧ r ∈ st1 → ¬ junkref(str, r, st1), ∀ r, ty. validref(str, r, ty, st0) → validref(str, r, ty, st1), r0 ∈ st0 → ¬ junkref(str, r0, st0) ⊦ r0 ∈ st

User applied rule cut formula

And obtained the following new goals

Proof step 13:
r0 ∈ st0, r0 ∈ st1, junkref(str, r0, st1), ∀ r, ty. validref(str, r, ty, st) → validref(str, r, ty, st0), ∀ r. ¬ r ∈ st0 ∧ r ∈ st1 → ¬ junkref(str, r, st1), ∀ r, ty. validref(str, r, ty, st0) → validref(str, r, ty, st1), r0 ∈ st0 → ¬ junkref(str, r0, st0) ⊦ r0 ∈ st
Proof step 15:
r0 ∈ st1, junkref(str, r0, st1), ∀ r, ty. validref(str, r, ty, st) → validref(str, r, ty, st0), ∀ r. ¬ r ∈ st0 ∧ r ∈ st1 → ¬ junkref(str, r, st1), ∀ r, ty. validref(str, r, ty, st0) → validref(str, r, ty, st1), r0 ∈ st0 → ¬ junkref(str, r0, st0) ⊦ r0 ∈ st0, r0 ∈ st

Rule argument

[fma-arg: r0 ∈ st0]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRAFMAS : (r0 ∈ st0)]]