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Proof step 5 from proof valid-sar-twice-same (conclusion)

⊦ valid(sar, ar) ∧ n < # ar ∧ m < # ar → (sar[n] = sar[m] ↔ n = m)

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : valid, , , ⊦ valid(sar, ar) ↔ sar .elems = bag< # ar ∧ (∀ n0, n1. n0 < # sar ∧ n1 < # sar → ( suffix (ar, sar[n0]) < suffix (ar, sar[n1]) ↔ n0 < n1))], [CSIMPNAMEDSEQ : sar-elems-bagle-size, , , ⊦ sar .elems = bag< n → # sar = n], [CSIMPNAMEDFORWARD : nat-basic1, , lf-01, ⊦ m < n ∧ n = n0 → m < n0], [CSIMPNAMEDSEQ : nat-basic1, , f, ⊦ m < n → n ≠ 0], [CSIMPNAMEDFORWARD : nat-basic1, , f, ⊦ m < n → n ≠ 0])]]