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Proof step 7 from proof swap-from-to (previous step)

#((σ from m) to n) = #((σ to m + n) from m), ⌜n0⌝ < #((σ from m) to n) ⊦ ((σ from m) to n)[n0] = ((σ to m + n) from m)[n0], # σ < ⌜m⌝ + ⌜n⌝

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
¬ # σ < ⌜n⌝ ⊦ #(σ to n) = ⌜n⌝
Proof step 9:
¬ ¬ #(σ from m) < ⌜n⌝ , #((σ from m) to n) = #((σ to m + n) from m), ⌜n0⌝ < #((σ from m) to n) ⊦ ((σ from m) to n)[n0] = ((σ to m + n) from m)[n0], # σ < ⌜m⌝ + ⌜n⌝
Proof step 14:
¬ #(σ from m) < ⌜n⌝ , ⌜n⌝ = #((σ to m + n) from m), ⌜n0⌝ < ⌜n⌝ ⊦ ((σ from m) to n)[n0] = ((σ to m + n) from m)[n0], # σ < ⌜m⌝ + ⌜n⌝

Rule argument

spec: inst: name: size-to seq: ¬ # σ < ⌜n⌝ ⊦ #(σ to n) = ⌜n⌝ subst: [n, σ] → [n, σ from m] flags: rewrite, current

Additional information

Used terms: n, σ from m