User module:Mattgately/Tau day

Proving theorems from Interface:Tau_day_theorems
 import (PROPOSITIONS Interface:Classical_propositional_calculus ) import (FIRSTORDER Interface:First-order_logic_with_quantifiability (PROPOSITIONS) ) import (TAU Interface:Tau_day_axioms (PROPOSITIONS FIRSTORDER) )

var (real θ) thm (TauIsPeriodOfSine     ( (         sin ( θ + (τ) )      ) = (          sin θ           ) )   (θ SinePeriod) )

var (real α) thm (TauIsPeriodOfSineQuarterTurn   ( (       sin        ( (             α               +               ((τ) / (4))           ) +          (τ) )    )      =      (        sin         ( α +          ((τ) / (4)) )     )  )    (       (α + ((τ) / (4)) ) SinePeriod ) )

thm (CosinePeriodLemma1     ( (         sin          ( (                θ                  +                  ( (τ) / (4) )              ) +             (τ) )      )       =       (          sin          ( (                θ                  +                  (τ)              ) +             ( (τ) / (4) ) )      )         )

(      θ ((τ) / (4)) (τ) Addition23       buildSine    ) )

thm (CosinePeriodLemma2   ( (       sin         ( (             θ              +              ( (τ) / (4) )           ) +          (τ) )    )     =     (        cos        (θ + (τ))     ) )

(     θ CosinePeriodLemma1      (θ + (τ)) SineShift      applyEqualityTransitivity   ) )

thm(CosinePeriod  ( (cos (θ + (τ))) = (cos θ) ) ( θ CosinePeriodLemma2 swapEquality ( θ + ((τ) / (4)) ) SinePeriod applyEqualityTransitivity θ SineShift applyEqualityTransitivity ))

thm(CosineTau  ( (cos (τ)) = (1) ) ( (τ) AdditiveIdentityLeft swapEquality buildCosine (0) CosinePeriod applyEqualityTransitivity Cosine0 applyEqualityTransitivity ))

export (THEOREMS Interface:Tau_day_theorems (PROPOSITIONS FIRSTORDER) ) 

Next page of proofs is: User_module:Mattgately/Tau_day2