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Proof step 42 from proof subset-size (previous step)

r ∈ st0 .refs, # st0 .refs ≤ # st1 .refs, r -- sk ∈ st0, r ∈ st0, rk ∈ st1, ∀ st. # st1 .refs ≤ # st .refs ∨ ¬ st1 ⊆ st, ∀ rk0. rk0 ∈ st1 -- (r -- sk) → rk0 ≠ r -- sk ∧ rk0 ∈ st0 ∧ st1[rk0] = st0[rk0] ⊦ st0 = ∅, r ∈ st1, rk ∈ st0 ∧ st1[rk] = st0[rk]

User applied rule all left

And closed the goal!

Rule argument

[EXRARG : pos: left 7, [extquanttermlist: (rk)abort:F, discard:F, computed:T]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ rk ∈ st -- rk0 ↔ rk ≠ rk0 ∧ rk ∈ st], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st])], [EXTRATERMS : (rk)]]