Nuprl Lemma : Game-minus-minus
∀G:Game. -(-(G)) ≡ G
Proof
Definitions occuring in Statement :
eq-Game: G ≡ H,
Game-minus: -(G),
Game: Game,
all: ∀x:A. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
member: t ∈ T,
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q,
all: ∀x:A. B[x],
or: P ∨ Q,
guard: {T},
eq-Game: G ≡ H,
and: P ∧ Q,
Game-minus: -(G),
right-move: right-move(g;x),
left-move: left-move(g;x),
left-indices: left-indices(g),
right-indices: right-indices(g),
mkGame: {mkGame(f[a] with a:L | g[b] with b:R},
Wsup: Wsup(a;b),
pi1: fst(t),
pi2: snd(t),
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)
Lemmas referenced :
Game-induction,
eq-Game_wf,
Game-minus_wf,
Game_wf,
left-option_wf,
right-option_wf,
left-move_wf,
right-indices_wf,
right-move_wf,
left-indices_wf,
eq-Game_inversion
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
sqequalRule,
lambdaEquality_alt,
cumulativity,
hypothesisEquality,
hypothesis,
universeIsType,
independent_functionElimination,
lambdaFormation_alt,
functionIsType,
inhabitedIsType,
unionIsType,
independent_pairFormation,
dependent_pairFormation_alt,
dependent_functionElimination,
inlFormation_alt,
equalityIstype,
productIsType,
inrFormation_alt,
because_Cache
Latex:
\mforall{}G:Game. -(-(G)) \mequiv{} G
Date html generated:
2019_10_31-AM-06_35_13
Last ObjectModification:
2019_09_12-PM-01_28_11
Theory : Numbers!and!Games
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