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Proof step 20 from proof validrefs-put-notin-02 (previous step)

st[r1 -- mkfs(class0, ty1, fieldvar0) '] = refval(r2), acc + r0 ' = r2 ' + refs, st[r1 -- _type] .type ≤ ty, is_obj(str, r1, st), okval(val, ty0), mkfs(class0, ty1, fieldvar0) ' ∈ instfields(st[r1 -- _type] .type .class), validrefs(str, r2 ' + refs, ty1, st), ∀ str, r0, ty, st, val, ty0, class, fieldvar, r. validrefs(str, acc + r0 ', ty, st) ∧ okval(val, ty0) → mkfs(class, ty0, fieldvar) ' = _length ∨ mkfs(class, ty0, fieldvar) ' = _type ∨ validrefs(str, acc + r0 ', ty, st[r -- mkfs(class, ty0, fieldvar) ', val]) ∨ r ∈ acc ⊦ r1 = jvmref, r = r1, mkfs(class, ty0, fieldvar) ' = _type, mkfs(class, ty0, fieldvar) ' = _length, r ∈ acc, validrefs(str, r2 ' + refs, ty1, st[r -- mkfs(class, ty0, fieldvar) ', val]), ¬ r2 ∈ acc ∧ r2 ≠ r0, r0 ≠ r2 ∧ ¬ r0 ∈ refs

User applied rule insert equation

And obtained the following new goals

Proof step 19:
st[r1 -- mkfs(class0, ty1, fieldvar0) '] = refval(r2), acc + r0 ' = r2 ' + refs, st[r1 -- _type] .type ≤ ty, is_obj(str, r1, st), okval(val, ty0), mkfs(class0, ty1, fieldvar0) ' ∈ instfields(st[r1 -- _type] .type .class), validrefs(str, acc + r0 ', ty1, st), ∀ str, r0, ty, st, val, ty0, class, fieldvar, r. validrefs(str, acc + r0 ', ty, st) ∧ okval(val, ty0) → mkfs(class, ty0, fieldvar) ' = _length ∨ mkfs(class, ty0, fieldvar) ' = _type ∨ validrefs(str, acc + r0 ', ty, st[r -- mkfs(class, ty0, fieldvar) ', val]) ∨ r ∈ acc ⊦ r1 = jvmref, r = r1, mkfs(class, ty0, fieldvar) ' = _type, mkfs(class, ty0, fieldvar) ' = _length, r ∈ acc, validrefs(str, acc + r0 ', ty1, st[r -- mkfs(class, ty0, fieldvar) ', val]), ¬ r2 ∈ acc ∧ r2 ≠ r0, r0 ≠ r2 ∧ ¬ r0 ∈ refs

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()]]