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Proof step 70 from proof validrefs-putshort-field (previous step)

r0 -- mkfs(class0, ty0, fieldvar0) ' ≠ r -- mkfs(class, short_type, fieldvar) ', st[r0 -- mkfs(class0, ty0, fieldvar0) '] = refval(r1), mkfs(class0, ty0, fieldvar0) ' ∈ instfields(st[r0 -- _type] .type .class), is_obj(str, r0, st), st[r0 -- _type] .type ≤ ty, is_obj(str, r0, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]), is_shortvalue(st[r -- mkfs(class, short_type, fieldvar) ']), validrefs(str, r1 ' + refs0, ty0, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]), r0 ≠ r ∨ class0 ≠ class ∨ ty0 ≠ short_type ∨ fieldvar0 ≠ fieldvar, ∀ sho, fieldvar, class, r, st, ty, str, refs. # refs < # (r0 + r1 + refs0) → ( validrefs(str, refs, ty, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]) ∧ is_shortvalue(st[r -- mkfs(class, short_type, fieldvar) ']) → refs = [] ∨ junkref(str, refs .first, st) ∨ validrefs(str, refs, ty, st)) ⊦ r0 = jvmref, junkref(str, r0, st), is_referencevalue(st[r0 -- mkfs(class0, ty0, fieldvar0) ']) ∧ r1 = st[r0 -- mkfs(class0, ty0, fieldvar0) '] .refval ∧ validrefs(str, st[r0 -- mkfs(class0, ty0, fieldvar0) '] .refval ' + refs0, ty0, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 62:
⊦ validrefs(str, refs, short_type, st) ↔ refs = [] ∨ refs = jvmref '
Proof step 69:
st[r0 -- mkfs(class0, ty0, fieldvar0) '] = refval(r1), validrefs(str, r1 ' + refs0, ty0, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]), is_shortvalue(st[r -- mkfs(class, short_type, fieldvar) ']), is_obj(str, r0, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]), st[r0 -- _type] .type ≤ ty, is_obj(str, r0, st), mkfs(class0, ty0, fieldvar0) ' ∈ instfields(st[r0 -- _type] .type .class), ∀ sho, fieldvar, class, r, st, ty, str, refs. # refs < # (r0 + r1 + refs0) → ( validrefs(str, refs, ty, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]) ∧ is_shortvalue(st[r -- mkfs(class, short_type, fieldvar) ']) → refs = [] ∨ junkref(str, refs .first, st) ∨ validrefs(str, refs, ty, st)) ⊦ r0 = jvmref, ty0 = short_type, junkref(str, r0, st), validrefs(str, r1 ' + refs0, ty0, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ mkfs(class1, ty, fieldvar) = mkfs(class2, ty0, fieldvar0) ↔ ¬ ¬ ( class1 = class2 ∧ ty = ty0 ∧ fieldvar = fieldvar0)], [CSIMPSEQ : ⊦ fs ' = fs0 ' ↔ fs = fs0], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)])]]