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Proof step 104 from proof validrefs-not-contains (previous step)

is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty, is_obj(str, r, st), r0 ' + refs0 + r1 ' = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ (r0 ' + refs0 + r1 ') .first = st[r -- fs '] .refval ∧ validrefs(str, r0 ' + refs0 + r1 ', fs .type, st)), st[r -- _type] .type ≤ ty, ∀ str0, st0, ty0. ¬ contains(str0, st0[r0 -- _type] .type, st0[r1 -- _type] .type) ∧ r0 ≠ r1 → ¬ validrefs(str0, r0 ' + refs0 + r1 ', ty0, st0) ⊦ r1 = jvmref, r = r1, r = jvmref, contains(str, st[r -- _type] .type, st[r1 -- _type] .type)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 103:
validrefs(str, st[r -- fs '] .refval ' + refs0 + r1 ', fs .type, st), is_referencevalue(st[r -- fs ']), fs ' ∈ instfields(st[r -- _type] .type .class), st[r -- _type] .type ≤ ty, is_obj(str, r, st), ∀ str0, st0, ty0. ¬ contains(str0, st0[st[r -- fs '] .refval -- _type] .type, st0[r1 -- _type] .type) ∧ st[r -- fs '] .refval ≠ r1 → ¬ validrefs(str0, st[r -- fs '] .refval ' + refs0 + r1 ', ty0, st0) ⊦ r = jvmref, r = r1, r1 = jvmref, contains(str, st[r -- _type] .type, st[r1 -- _type] .type)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []])]]