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Proof step 53 from proof bitsand-cast (previous step)

n = # fillsgn(n, mklist(boolvar, n0 - 1) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0)), n = # fillsgn(n, mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1), sgn(mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1) = boolvar ' + boolvar0 ' + bits1, n + 1 < n0 + # bitsand(boolvar ' + boolvar0 ' + bits1, bits0), (n0 - 1) + # bitsand(boolvar ' + boolvar0 ' + bits1, bits0) < n, n0 + 1 + # bits1 < n, bits0.first, # bits0 ≤ 2 + # bits1, # bitsand(boolvar ' + boolvar0 ' + bits1, bits0) < n ⊦ mklist(boolvar, n - # bitsand(boolvar ' + boolvar0 ' + bits1, bits0)) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0) = fillsgn(n, mklist(boolvar, n0 - 1) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0)), bits0 = [], boolvar ↔ boolvar0, n0 = 0, boolvar ∧ boolvar0

User applied rule insert elim lemma

And closed the goal!

Rule argument

seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [n0, m] rotate: T spec: nat inst: name: elim-pred-c

Additional information

Used simplifier rules: ⊦ m + 1 ≠ 0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ m + n < m + n0 ↔ n < n0;% ⊦ m < n → ¬ n < m;%n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n0, m