Nuprl Lemma : eq-Game_transitivity
∀G,H,K:Game.  (G ≡ H 
⇒ H ≡ K 
⇒ G ≡ K)
Proof
Definitions occuring in Statement : 
eq-Game: G ≡ H
, 
Game: Game
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
so_lambda: λ2x.t[x]
, 
member: t ∈ T
, 
prop: ℙ
, 
implies: P 
⇒ Q
, 
so_apply: x[s]
, 
all: ∀x:A. B[x]
, 
guard: {T}
, 
eq-Game: G ≡ H
, 
and: P ∧ Q
, 
cand: A c∧ B
, 
exists: ∃x:A. B[x]
, 
right-option: right-option{i:l}(g;m)
, 
left-option: left-option{i:l}(g;m)
, 
or: P ∨ Q
Lemmas referenced : 
Game-induction, 
all_wf, 
Game_wf, 
eq-Game_wf, 
or_wf, 
left-option_wf, 
right-option_wf, 
left-indices_wf, 
right-indices_wf, 
left-move_wf, 
equal_wf, 
exists_wf, 
right-move_wf, 
eq-Game_inversion
Rules used in proof : 
cut, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isectElimination, 
thin, 
sqequalRule, 
lambdaEquality, 
instantiate, 
hypothesis, 
cumulativity, 
functionEquality, 
hypothesisEquality, 
independent_functionElimination, 
lambdaFormation, 
comment, 
productElimination, 
dependent_functionElimination, 
independent_pairFormation, 
dependent_pairFormation, 
inlFormation, 
inrFormation, 
because_Cache
Latex:
\mforall{}G,H,K:Game.    (G  \mequiv{}  H  {}\mRightarrow{}  H  \mequiv{}  K  {}\mRightarrow{}  G  \mequiv{}  K)
Date html generated:
2018_05_22-PM-09_53_26
Last ObjectModification:
2018_05_20-PM-10_40_31
Theory : Numbers!and!Games
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