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Proof step 10 from proof pathex-array (previous step)

validrefs(str, st[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st), is_referencevalue(st[r -- i ']), i < st[r -- _length] .intval, is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i ⊦ r = (st[r -- i '] .refval ' + refs) .last, st[r -- i '] .refval ≠ jvmref ∧ (¬ is_valid_ref(str, st[r -- i '] .refval, st) ∨ ¬ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type), st[r -- i '] .refval = jvmref ∧ (st[r -- i '] .refval ' + refs) .last = jvmref, st[r -- i '] .refval ≠ jvmref ∧ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∧ path∃(str, st[r -- i '] .refval, (st[r -- i '] .refval ' + refs) .last, st)

User applied rule cut formula

And obtained the following new goals

Proof step 8:
st[r -- i '] .refval ≠ jvmref, validrefs(str, st[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st), is_referencevalue(st[r -- i ']), i < st[r -- _length] .intval, is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i ⊦ r = (st[r -- i '] .refval ' + refs) .last, st[r -- i '] .refval ≠ jvmref ∧ (¬ is_valid_ref(str, st[r -- i '] .refval, st) ∨ ¬ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type), st[r -- i '] .refval = jvmref ∧ (st[r -- i '] .refval ' + refs) .last = jvmref, st[r -- i '] .refval ≠ jvmref ∧ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∧ path∃(str, st[r -- i '] .refval, (st[r -- i '] .refval ' + refs) .last, st)
Proof step 9:
⊦ validrefs(str, jvmref ' + refs, ty, st) ↔ refs = []

Rule argument

[fma-arg: st[r -- i '] .refval ≠ jvmref]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ refs + [] = refs], [CSIMPSEQ : ⊦ r ' .last = r])], [EXTRAFMAS : (st[r -- i '] .refval ≠ jvmref)]]