Nuprl Lemma : eq-Game_inversion
∀G,H:Game. (G ≡ H ⇒ H ≡ G)
Proof
Definitions occuring in Statement :
eq-Game: G ≡ H,
Game: Game,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
eq-Game: G ≡ H,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
cand: A c∧ B,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x]
Lemmas referenced :
all_wf,
left-indices_wf,
exists_wf,
eq-Game_wf,
left-move_wf,
right-indices_wf,
right-move_wf,
Game_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
hypothesis,
independent_pairFormation,
productEquality,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
lambdaEquality
Latex:
\mforall{}G,H:Game. (G \mequiv{} H {}\mRightarrow{} H \mequiv{} G)
Date html generated:
2018_05_22-PM-09_53_21
Last ObjectModification:
2018_05_20-PM-10_40_12
Theory : Numbers!and!Games
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