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Proof step 12 from proof validsubset-trans (previous step)

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 ∈ st, junkref(str, r0, st0)

User applied rule all left

And obtained the following new goals

Proof step 11:
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), validref(str, r0, st0[r0 -- _type] .type, st0) → validref(str, r0, st0[r0 -- _type] .type, st1) ⊦ r0 ∈ st, junkref(str, r0, st0)

Rule argument

[EXRARG : pos: left 6, [extquanttermlist: (r0, st0[r0 -- _type] .type) abort:F , discard:T , computed:F ]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r0, st0[r0 -- _type] .type)]]