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Proof step 58 from proof pathex-put-cyclic (previous step)

st[(r ' + refs1) .last -- _type] .type = mkclasstype(class0), mkfs(class, ty, fieldvar) ' ∈ instfields(class0), st[r -- _type] .type ≤ ty, validrefs(str, r ' + refs1, st[r -- _type] .type, st) ⊦ r = jvmref, (r ' + refs1) .last = jvmref, r = (r ' + refs1) .last, dups(refs1), r ∈ refs1, ∃ refs. dups(refs) ∧ refs .first = (r ' + refs1) .last ∧ validrefs (str, refs, (st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r)][refs .first -- _type]) .type, st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r)])

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 57:
st[(r ' + refs1) .last -- _type] .type = mkclasstype(class0), mkfs(class, ty, fieldvar) ' ∈ instfields(class0), st[r -- _type] .type ≤ ty, validrefs(str, r ' + refs1, st[r -- _type] .type, st) ⊦ refs1 = [], r = jvmref, (r ' + refs1) .last = jvmref, r = (r ' + refs1) .last, dups(refs1), r ∈ refs1, ∃ refs. dups(refs) ∧ refs .first = (r ' + refs1) .last ∧ validrefs (str, refs, (st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r)][refs .first -- _type]) .type, st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r)])

Rule argument

[fma-arg: refs1 = []]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ refs + [] = refs], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' .last = r])], [EXTRAFMAS : (refs1 = [])]]