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Proof step 14 from proof mon-lem (previous step)

σσ[m] + σ = σσ[m1 + m], σσ[m1 + m] + σ0 = σσ[(m1 + m) + 1], ⌜m1⌝ + ⌜1⌝ + ⌜m⌝ < # σσ, ⌜m1⌝ + ⌜m⌝ < # σσ, ∀ n. ⌜n⌝ + ⌜1⌝ < # σσ → (∃ σ1. σσ[n] + σ1 = σσ[n + 1]) ⊦ σσ[m] + σ + σ0 = σσ[(m1 + 1) + m]

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: nat-basic2 inst: name: a seq: ⊦ (m + n0) + n1 = m + n0 + n1 subst: [n1, n0, m] → [m, 1, m1] flags: rewrite

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used terms: m, 1, m1