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Proof step 81 from proof bitsand-cast-01 (previous step)

# bits1 < # bitsand(bits1, true ' + bits), # bits < # bitsand(bits1, true ' + bits), # bits < # bits1, # bits + 1 < # bitsand(bits1, true ' + bits) ⊦ # bits1 = # bitsand(bits1, true ' + bits), bits1 = [], bits2 = [], bits2 + bits1 = [], lastn(# bits1, bitsand(bits1, true ' + bits)) = lastn(# bits1, fillsgn(# bits1, bits2 + bitsand(bits1, true ' + bits)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 82:
⊦ bits0.first ∧ # bits0 ≤ # bits ∧ bits0 ≠ [] → # bitsand(bits, bits0) = # bits

Rule argument

name: bitsand-len-true rotate: F subst: [bits0, bits] → [true ' + bits, bits1]

Additional information

Used simplifier rules: ⊦ (boolvar ' + bits).first ↔ boolvar;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ m + 1 ≤ n ↔ m < n;% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m < n → (n ≤ m ↔ false);% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ boolvar ' ≠ []; Used terms: true ' + bits, bits1