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Proof step 48 from proof validrefs-put-notin-01 (previous step)

st[r1 -- i '] = refval(r4), acc + r0 ' = r4 ' + refs, 0 < st[r1 -- _length] .intval, 0 ≤ i, st[r1 -- _type] .type ≤ ty, okval(val, ty1), r -- mkfs(class, ty1, fieldvar) ' ∈ st, okval(st[r -- mkfs(class, ty1, fieldvar) '], ty1), r ∈ st, is_array(str, r1, st), validrefs(str, r4 ' + refs, st[r1 -- _type] .type .type, st[r -- mkfs(class, ty1, fieldvar) ', val]), i < st[r1 -- _length] .intval, ∀ r2, fs0, val0, st0, str0, r3, ty0. ¬ r2 ∈ acc ∧ fs0 ' ≠ _type ∧ fs0 ' ≠ _length ∧ okval(val0, fs0 .type) ∧ r2 -- fs0 ' ∈ st0 ∧ okval(st0[r2 -- fs0 '], fs0 .type) → (validrefs(str0, acc + r3 ', ty0, st0[r2 -- fs0 ', val0]) ↔ validrefs(str0, acc + r3 ', ty0, st0)) ⊦ r = r1, r1 = jvmref, mkfs(class, ty1, fieldvar) ' = _length, mkfs(class, ty1, fieldvar) ' = _type, r ∈ acc, validrefs(str, r4 ' + refs, st[r1 -- _type] .type .type, st), ¬ r4 ∈ acc ∧ r4 ≠ r0, r0 ≠ r4 ∧ ¬ r0 ∈ refs

User applied rule insert equation

And obtained the following new goals

Rule argument

[inserteqarg: pos: left 2,T,F,()]

Additional information

[[CONCRETESIMPRULES : ()]]