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Proof step 74 from proof validrefs-put-notin-03 (previous step)

¬ (r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty)), is_valid_ref(str, r, st) ↔ is_valid_ref(str, r, st[r -- sk, val]) ⊦ r = r0, val .refval = r0, r0 = st[r -- sk] .refval, sk = _type, sk = _length, validrefs(str, r ' + r0 ' + refs1, ty, st[r -- sk, val]) ↔ validrefs(str, r ' + r0 ' + refs1, ty, st), r ∈ refs1, dups(refs1), r0 ∈ refs1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ validrefs(str, jvmref ' + refs, ty, st) ↔ refs = []
Proof step 73:
is_valid_ref(str, r, st), st[r -- _type] .type ≤ ty, is_valid_ref(str, r, st[r -- sk, val]) ⊦ r = r0, val .refval = r0, r0 = st[r -- sk] .refval, sk = _type, sk = _length, validrefs(str, r ' + r0 ' + refs1, ty, st[r -- sk, val]) ↔ validrefs(str, r ' + r0 ' + refs1, ty, st), r = jvmref, r ∈ refs1, dups(refs1), r0 ∈ refs1

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPNAMEDSEQ : list, references, e, ⊦ r ' ≠ []], [CSIMPNAMEDSEQ : list, references, app-02-ant, ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPNAMEDSEQ : addfuns, , is_valid_ref-null, ⊦ ¬ is_valid_ref (str, jvmref, st)])]]