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Proof step 23 from proof bitsor-mklist-in (previous step)

∀ bits, boolvar0, boolvar, n, bits1. # bits1 < # bits0 → true → n = 0 ∨ bits1 = [] ∨ (boolvar ∈ bitsor(mklist(boolvar0, n) + bits, bits1) ↔ boolvar ∈ bitsor(boolvar0 ' + bits, bits1)) ⊦ # bits0 = 1, bits0 = [], boolvar ∈ bitsor(mklist(boolvar0, n - 1), bits0.butlast) ∨ (boolvar ↔ boolvar0 ∨ bits0.last) ↔ boolvar ∈ bitsor(boolvar0 ', bits0), n = 0, n = 1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 24:
n = m + 1, ∀ bits, boolvar0, boolvar, n, bits1. # bits1 < # bits0 → true → n = 0 ∨ bits1 = [] ∨ (boolvar ∈ bitsor(mklist(boolvar0, n) + bits, bits1) ↔ boolvar ∈ bitsor(boolvar0 ' + bits, bits1)) ⊦ # bits0 = 1, bits0 = [], boolvar ∈ bitsor(mklist(boolvar0, m), bits0.butlast) ∨ (boolvar ↔ boolvar0 ∨ bits0.last) ↔ boolvar ∈ bitsor(boolvar0 ', bits0), n = 0, n = 1

Rule argument

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

Additional information

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