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Proof step 3 from proof append-to-gr-01 (previous step)

# x < m ⊦ ⌜x⌝ + σ to m = ⌜x⌝ + (σ to (m - # x))

User applied rule structural induction

And obtained the following new goals

Proof step 4:
#(a + x0) < m, ∀ m, σ. # x0 < m → ⌜x0⌝ + σ to m = ⌜x0⌝ + (σ to (m - # x0)) ⊦ ⌜a + x0⌝ + σ to m = ⌜a + x0⌝ + (σ to (m - #(a + x0)))

Rule argument

indvar: x

Additional information

Used simplifier rules: empty: ⊦ ⌜[]⌝ = [];%empty-append: ⊦ [] + σ = σ;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%list freely generated by [], +;;% ⊦ # [] = 0; (s)% ⊦ m - 0 = m; (s)