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Proof step 21 from proof validsubset-trans (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
∀ r, ty. validref(str, r, ty, st0) → validref(str, r, ty, st1), ∀ r. ¬ r ∈ st0 ∧ r ∈ st1 → ¬ junkref(str, r, st1), ∀ r. ¬ r ∈ st ∧ r ∈ st0 → ¬ junkref(str, r, st0), ∀ r, ty. validref(str, r, ty, st) → validref(str, r, ty, st0) ⊦ (validref(str, r, ty, st) → validref(str, r, ty, st1)) ∧ (¬ r0 ∈ st ∧ r0 ∈ st1 → ¬ junkref(str, r0, st1))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]