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Proof step 18 from proof cyclic-put-nopathex (previous step)

validrefs(str, (r ' + refs1) + r1 ', st[r -- _type] .type, st[r0 -- sk, val]) ⊦ sk = _type, path∃(str, r, r0, st), junkref(str, r, st), dups(refs1), r ∈ refs1, ∃ refs0, r1. ¬ dups(refs0) ∧ r1 ∈ refs0 ∧ refs0 .first = r ∧ validrefs(str, refs0 + r1 ', st[refs0 .first -- _type] .type, st), r1 ≠ r ∧ ¬ r1 ∈ refs1

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 17:
validrefs(str, (r ' + refs1) + r1 ', st[r -- _type] .type, st[r0 -- sk, val]) ⊦ r -- _type = r0 -- sk, sk = _type, path∃(str, r, r0, st), junkref(str, r, st), dups(refs1), r ∈ refs1, ∃ refs0, r1. ¬ dups(refs0) ∧ r1 ∈ refs0 ∧ refs0 .first = r ∧ validrefs(str, refs0 + r1 ', st[refs0 .first -- _type] .type, st), r1 ≠ r ∧ ¬ r1 ∈ refs1

Rule argument

[fma-arg: r -- _type = r0 -- sk]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0])], [EXTRAFMAS : (r -- _type = r0 -- sk)]]