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Proof step 10 from proof cyclic-put-statfield-01 (previous step)

validrefs(str, r ' + refs0, st[r -- _type] .type, st) ⊦ ¬ r ∈ refs0 ∧ ¬ dups(refs0), (dups(refs0) ∨ r ∈ refs0) ∧ validrefs(str, r ' + refs0, (st[jvmref -- sk, val][r -- _type]) .type, st)

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 5:
⊦ validrefs(str, jvmref ' + refs, ty, st) ↔ refs = []
Proof step 9:
validrefs(str, r ' + refs0, st[r -- _type] .type, st) ⊦ r -- _type = jvmref -- sk, ¬ r ∈ refs0 ∧ ¬ dups(refs0), (dups(refs0) ∨ r ∈ refs0) ∧ validrefs(str, r ' + refs0, (st[jvmref -- sk, val][r -- _type]) .type, st)

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ (st[rk, val][rk]) = val])], [EXTRAFMAS : (r -- _type = jvmref -- sk)]]