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Proof step 79 from proof bitsand-cast (previous step)

n = # fillsgn(n, mklist(boolvar, m) + boolvar ' + boolvar0 ' + bits1), sgn(mklist(boolvar, m) + boolvar ' + boolvar0 ' + bits1) = boolvar ' + boolvar0 ' + bits1, # bits0 + 1 < m + # bitsand(boolvar ' + boolvar0 ' + bits1, bits0), # bits0 < m + # bitsand(boolvar ' + boolvar0 ' + bits1, bits0), # bits0 + 1 < n, 3 + # bits1 < m + # bitsand(boolvar ' + boolvar0 ' + bits1, bits0), bits0.first, # bits0 ≤ 2 + # bits1, # bitsand(boolvar ' + boolvar0 ' + bits1, bits0) < n, n ≤ m + # bitsand(boolvar ' + boolvar0 ' + bits1, bits0), 2 + # bits1 < # bitsand(boolvar ' + boolvar0 ' + bits1, bits0), 2 + # bits1 + m < n, # bits0 < # bitsand(boolvar ' + boolvar0 ' + bits1, bits0), 3 + # bits1 < n, 2 + # bits1 < n, # bits0 < n ⊦ mklist(boolvar, n - # bitsand(boolvar ' + boolvar0 ' + bits1, bits0)) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0) = lastn(n, mklist(boolvar, m) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0)), m = 0, bits0 = [], boolvar ↔ boolvar0, boolvar ∧ boolvar0

User applied rule insert elim lemma

And obtained the following new goals

Rule argument

seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n, # bitsand(boolvar ' + boolvar0 ' + bits1, bits0), n0] rotate: T spec: nat inst: name: elim-sub

Additional information

Used simplifier rules: ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n → ¬ n < m;%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n, # bitsand(boolvar ' + boolvar0 ' + bits1, bits0), n0