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Proof step 3 from proof to-to-leq (previous step)

m ≤ n ⊦ ⌜x⌝ to n to m = ⌜x⌝ to m, # ⌜x⌝ < ⌜n⌝

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
m ≤ n, n ≤ # x, m ≤ # x ⊦ x to n to m = x to m

Rule argument

Additional information

Used simplifier rules: to-fin: ⊦ ⌜x⌝ to n = ⌜x to n⌝ ;%size-fin: ⊦ # ⌜x⌝ = ⌜# x⌝ ;%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; from specification nat-inf%inj-02: ⊦ ⌜x⌝ = ⌜x0⌝ ↔ x = x0; from specification stream-basic