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Proof step 7 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) ⊦ validref(str, r, ty, st) → validref(str, r, ty, st1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
validref(str, r, ty, st), ∀ r, ty. validref(str, r, ty, st) → validref(str, r, ty, st0), ∀ r. ¬ r ∈ st ∧ r ∈ st0 → ¬ junkref(str, r, st0), ∀ r. ¬ r ∈ st0 ∧ r ∈ st1 → ¬ junkref(str, r, st1), ∀ r, ty. validref(str, r, ty, st0) → validref(str, r, ty, st1) ⊦ validref(str, r, ty, st1)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]