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Proof step 7 from proof append-to-gr-01 (previous step)

# x0 + 1 < m, ∀ m, σ. # x0 < m → ⌜x0⌝ + σ to m = ⌜x0⌝ + (σ to (m - # x0)) ∨ m = 0 ⊦ m = 0, ⌜x0⌝ + σ to (m - 1) = ⌜x0⌝ + (σ to (m - # x0 + 1))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
m = m0 + 1, # x0 + 1 < m, ∀ m, σ. # x0 < m → ⌜x0⌝ + σ to m = ⌜x0⌝ + (σ to (m - # x0)) ∨ m = 0 ⊦ m = 0, ⌜x0⌝ + σ to m0 = ⌜x0⌝ + (σ to (m - # x0 + 1))

Rule argument

spec: nat inst: name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [m, m1] flags:

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: m, m1