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Proof step 9 from proof int2bits-falsein-01 (previous step)

uint2bits(~ i) = bits + true ' + bits0, bitsinvert(uint2bits(~ i)) +1 = bitsinvert(bits) + true ' + bits0, i < 0, i < ~1 ⊦ bits = [], true ∈ bits0, false ∈ sgn(bitsinvert(bits) + true ' + bits0).rest

User applied rule cut formula

And obtained the following new goals

Proof step 10:
bits.first, uint2bits(~ i) = bits + true ' + bits0, bitsinvert(uint2bits(~ i)) +1 = bitsinvert(bits) + true ' + bits0, i < 0, i < ~1 ⊦ bits = [], true ∈ bits0, false ∈ sgn(bitsinvert(bits) + true ' + bits0).rest
Proof step 11:
uint2bits(~ i) = bits + true ' + bits0, bitsinvert(uint2bits(~ i)) +1 = bitsinvert(bits) + true ' + bits0, i < 0, i < ~1 ⊦ bits.first, bits = [], true ∈ bits0, false ∈ sgn(bitsinvert(bits) + true ' + bits0).rest

Rule argument

fma: bits.first

Additional information

Used formulas: bits.first