i need to prove that if x is the first of sub([tex]\phi[/tex];a,[tex]\psi[/tex]) then there exists 1<=i<=n and there exist firsts [tex]\phi' of \phi_i and \psi' for \psi[/tex] such that x=sub([tex]\phi';a,\psi[/tex])[tex]\psi'[/tex](adsbygoogle = window.adsbygoogle || []).push({});

where sub(t;a,b) is defined as follows:

let a1,..,an be n signs and b1,..,bn expressions.

a=(a1,...,an)

b=(b1,..,bn)

the substitution sub(t;a,b) is defined as:

if t is t1,...,tk then sub(t;a,b)=x1x2...xk

when 1<=i<=k xi is bj if ti=aj and xi is ti when ti isnt in {a1,...,an}.

what i did is as follows:

x is the first of sub(t;a,b) then there exists y such that sub(t;a,b)=xy

and let t' be the first of t, then t=t'z and thuse we can deduce that:

sub(t;a,b)=sub(t';a,b)sub(z;a,b)=xy

but i dont know how to procceed from here.

thanks in davance.

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A question in substitution in logic.

Loading...

Similar Threads for question substitution logic | Date |
---|---|

B What question should you ask? | Apr 16, 2018 |

I Question about simplifying Sigma notation | Feb 11, 2018 |

I Shopping List Game: Probability Question | Dec 10, 2017 |

I A simple question about probability theory | Aug 2, 2017 |

Cracking a monoalphabetic substitution cipher | Aug 12, 2012 |

**Physics Forums - The Fusion of Science and Community**